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13 <html xmlns="http://www.w3.org/1999/xhtml">
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14 <head>
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15 <title>Math - The Commons Math User Guide - Complex Numbers</title>
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28 Commons Math User Guide
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66
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67 <h5>User Guide</h5>
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68 <ul>
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70 <li class="none">
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71 <a href="../userguide/index.html">Contents</a>
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100 </li>
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101
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102 <li class="none">
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103 <strong>Complex Numbers</strong>
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104 </li>
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146 </div>
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147 <div id="bodyColumn">
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148 <div id="contentBox">
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149 <div class="section"><h2><a name="a7_Complex_Numbers"></a>7 Complex Numbers</h2>
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150 <div class="section"><h3><a name="a7.1_Overview"></a>7.1 Overview</h3>
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151 <p>
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152 The complex packages provides a complex number type as well as complex
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153 versions of common transcendental functions and complex number
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154 formatting.
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155 </p>
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156 </div>
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157 <div class="section"><h3><a name="a7.2_Complex_Numbers"></a>7.2 Complex Numbers</h3>
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158 <p><a href="../apidocs/org/apache/commons/math/complex/Complex.html">
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159 org.apache.commons.math.complex.Complex</a> provides a complex number
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160 type that forms the basis for the complex functionality found in
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161 commons-math.
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162 </p>
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163 <p>
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164 Complex functions and arithmetic operations are implemented in
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165 commons-math by applying standard computational formulas and
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166 following the rules for <code>java.lang.Double</code> arithmetic in
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167 handling infinite and <code>NaN</code> values. No attempt is made
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168 to comply with ANSII/IEC C99x Annex G or any other standard for
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169 Complex arithmetic. See the class and method javadocs for the
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170 <a href="../apidocs/org/apache/commons/math/complex/Complex.html">
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171 Complex</a> and
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172 <a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html">
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173 ComplexUtils</a> classes for details on computing formulas.
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174 </p>
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175 <p>
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176 To create a complex number, simply call the constructor passing in two
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177 floating-point arguments, the first being the real part of the
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178 complex number and the second being the imaginary part:
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179 <div class="source"><pre>Complex c = new Complex(1.0, 3.0); // 1 + 3i</pre>
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180 </div>
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181 </p>
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182 <p>
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183 Complex numbers may also be created from polar representations
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184 using the <code>polar2Complex</code> method in
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185 <code>ComplexUtils</code>.
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186 </p>
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187 <p>
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188 The <code>Complex</code> class provides basic unary and binary
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189 complex number operations. These operations provide the means to add,
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190 subtract, multiply and divide complex numbers along with other
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191 complex number functions similar to the real number functions found in
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192 <code>java.math.BigDecimal</code>:
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193 <div class="source"><pre>Complex lhs = new Complex(1.0, 3.0);
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194 Complex rhs = new Complex(2.0, 5.0);
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195
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196 Complex answer = lhs.add(rhs); // add two complex numbers
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197 answer = lhs.subtract(rhs); // subtract two complex numbers
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198 answer = lhs.abs(); // absolute value
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199 answer = lhs.conjugate(rhs); // complex conjugate</pre>
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200 </div>
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201 </p>
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202 </div>
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203 <div class="section"><h3><a name="a7.3_Complex_Transcendental_Functions"></a>7.3 Complex Transcendental Functions</h3>
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204 <p><a href="../apidocs/org/apache/commons/math/complex/Complex.html">
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205 org.apache.commons.math.complex.Complex</a> also provides
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206 implementations of serveral transcendental functions involving complex
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207 number arguments. Prior to version 1.2, these functions were provided
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208 by <a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html">
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209 org.apache.commons.math.complex.ComplexUtils</a> in a way similar to the real
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210 number functions found in <code>java.lang.Math</code>, but this has been
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211 deprecated. These operations provide the means to compute the log, sine,
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212 tangent, and other complex values :
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213 <div class="source"><pre>Complex first = new Complex(1.0, 3.0);
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214 Complex second = new Complex(2.0, 5.0);
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215
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216 Complex answer = first.log(); // natural logarithm.
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217 answer = first.cos(); // cosine
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218 answer = first.pow(second); // first raised to the power of second</pre>
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219 </div>
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220 </p>
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221 </div>
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222 <div class="section"><h3><a name="a7.4_Complex_Formatting_and_Parsing"></a>7.4 Complex Formatting and Parsing</h3>
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223 <p><code>Complex</code> instances can be converted to and from strings
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224 using the<a href="../apidocs/org/apache/commons/math/complex/ComplexFormat.html">
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225 org.apache.commons.math.complex.ComplexFormat</a> class.
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226 <code>ComplexFormat</code> is a <code>java.text.Format</code>
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227 extension and, as such, is used like other formatting objects (e.g.
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228 <code>java.text.SimpleDateFormat</code>):
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229 <div class="source"><pre>ComplexFormat format = new ComplexFormat(); // default format
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230 Complex c = new Complex(1.1111, 2.2222);
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231 String s = format.format(c); // s contains "1.11 + 2.22i"</pre>
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232 </div>
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233 </p>
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234 <p>
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235 To customize the formatting output, one or two
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236 <code>java.text.NumberFormat</code> instances can be used to construct
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237 a <code>ComplexFormat</code>. These number formats control the
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238 formatting of the real and imaginary values of the complex number:
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239 <div class="source"><pre>NumberFormat nf = NumberFormat.getInstance();
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240 nf.setMinimumFractionDigits(3);
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241 nf.setMaximumFractionDigits(3);
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242
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243 // create complex format with custom number format
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244 // when one number format is used, both real and
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245 // imaginary parts are formatted the same
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246 ComplexFormat cf = new ComplexFormat(nf);
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247 Complex c = new Complex(1.11, 2.2222);
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248 String s = format.format(c); // s contains "1.110 + 2.222i"
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249
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250 NumberFormat nf2 = NumberFormat.getInstance();
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251 nf.setMinimumFractionDigits(1);
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252 nf.setMaximumFractionDigits(1);
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253
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254 // create complex format with custom number formats
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255 cf = new ComplexFormat(nf, nf2);
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256 s = format.format(c); // s contains "1.110 + 2.2i"</pre>
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257 </div>
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258 </p>
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259 <p>
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260 Another formatting customization provided by
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261 <code>ComplexFormat</code> is the text used for the imaginary
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262 designation. By default, the imaginary notation is "i" but, it can be
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263 manipulated using the <code>setImaginaryCharacter</code> method.
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264 </p>
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265 <p>
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266 Formatting inverse operation, parsing, can also be performed by
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267 <code>ComplexFormat</code>. Parse a complex number from a string,
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268 simply call the <code>parse</code> method:
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269 <div class="source"><pre>ComplexFormat cf = new ComplexFormat();
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270 Complex c = cf.parse("1.110 + 2.222i");</pre>
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271 </div>
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272 </p>
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273 </div>
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274 </div>
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276 </div>
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282 <div class="xright">©
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283 2003-2010
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