Example: Complex Numbers, Polar Notation

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Example: Complex Numbers, Polar Notation

Use the complex number functions to construct a complex number, show its polar form, and find its conjugate.

1. Enter a complex number:

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For the imaginary unit, type a constant immediately followed by i or j, such as "1i" or "1j." Click in the complex number expression above and notice that "2i" is really 2i, not 2* i, which defines it as the imaginary unit and not 2 times the variable i.

2. Show the polar form of z:

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3. Reconstruct the original rectangular form:

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<region id="ID0E15KQ" top="480" left="24" height="25.6" width="309.053333333333" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="7">
    <eval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <mult />
          <apply>
            <absval />
            <id>z</id>
          </apply>
          <apply>
            <id>cos</id>
            <apply>
              <id>arg</id>
              <id>z</id>
            </apply>
          </apply>
        </apply>
        <apply>
          <mult />
          <apply>
            <absval />
            <id>z</id>
          </apply>
          <apply>
            <scale />
            <apply>
              <id>sin</id>
              <apply>
                <id>arg</id>
                <id>z</id>
              </apply>
            </apply>
            <imag symbol="i">1</imag>
          </apply>
        </apply>
      </apply>
      <unitOverride>
        <placeholder />
      </unitOverride>
    </eval>
  </math>
</region>

4. Find the conjugate of z by subtracting its imaginary component from its real component:

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5. Use the conjugate operator to find the conjugate of z:

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