Writing Complex Numbers in Standard Form

Symbolics > Working with Symbolics > Simplifying and Rewriting Expressions > Writing Complex Numbers in Standard Form

• Use the keyword rectangular to write a complex number in standard, rectangular form, a+bi.

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  <math resultRef="3">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">ln</id>
        <apply>
          <plus />
          <real>1</real>
          <imag symbol="i">1</imag>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">rectangular</id>
      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <id labels="FUNCTION" xml:space="preserve">ln</id>
            <apply>
              <nthRoot />
              <placeholder />
              <real>2</real>
            </apply>
          </apply>
          <apply>
            <mult />
            <apply>
              <div />
              <id labels="CONSTANT" xml:space="preserve">π</id>
              <real>4</real>
            </apply>
            <imag symbol="i">1</imag>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

The returned answer is in the standard, rectangular form a+bi, where a and b are the real and imaginary parts of the complex number, respectively.

• Evaluate the following complex conjugate.

• Use the keyword rectangular to evaluate the same complex conjugate.

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  <math resultRef="5">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <conjugate />
        <parens>
          <apply>
            <plus />
            <id xml:space="preserve">a</id>
            <apply>
              <mult />
              <id xml:space="preserve">b</id>
              <imag symbol="i">1</imag>
            </apply>
          </apply>
        </parens>
      </apply>
      <command>
        <id xml:space="preserve">rectangular</id>
      </command>
      <symResult>
        <apply>
          <minus />
          <id labels="*" xml:space="preserve">a</id>
          <apply>
            <mult />
            <id labels="*" xml:space="preserve">b</id>
            <imag symbol="i">1</imag>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

The returned answer is in the standard rectangular form a+bi.