11.2 Geometric Representations of Complex Numbers

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11.2 Geometric Representations of Complex Numbers
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Graphing Complex Numbers

• In Algebra 2, you learned how to graph a complex
  number

Imaginary Part
Real Part
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Graphing Complex Numbers

• Graph the point 5 - 7i

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A point representing a complex number can be
written 2 different ways

• 1.) Rectangular Form
• z a bi
• 2.) Polar Form
• z r cos(?) r sin(?)i
• Polar form is often simplified by factoring out
  the radius.
• z r cis(?)

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Covert each complex number to polar form
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Covert each complex number to rectangular form
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Products of Complex Numbers
Back in Algebra 2, you learned how to multiply
complex numbers
Foil This
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Products of Complex Numbers in Polar Form
Lets multiply 2 complex numbers
Reorder the terms
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Products of Complex Numbers in Polar Form
Reorder the terms
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Products of Complex Numbers in Polar Form
Translation When you multiply complex numbers in
polar form, you simply multiply the radii add
the angles.
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Multiply using the polar form of the complex
number
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Multiply using the polar form of the complex
number
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Multiply using the polar form of the complex
number