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GEOMETRIC REPRESENTATION OF COMPLEX NUMBERS A Complex Number is in the form: z = a+bi We can graph complex numbers on the axis shown below: Real axis Imaginary Axis

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ABSOLUTE VALUE OF A COMPLEX NUMBER An arrow is drawn from the origin to represent the complex number. The length of the arrow is the absolute value of the complex number.

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REPRESENTING COMPLEX NUMBERS USING RECTANGULAR VS. POLAR COORDINATES So, We abbreviate this as cis

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Complex Numbers Rectangular Form: Polar Form:

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Example: Convert to rectangular form. Formulas:

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Example: Convert to polar form. Formulas:

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Example: What is the absolute value of the following complex numbers:

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Multiply:

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Do you want to go thru that every time? No!

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Multiply:

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Divide:

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SUMMARY To convert a+bi to polar: To convert to rectangular: Formulas: Formulas:

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9.7 PRODUCTS AND QUOTIENTS OF COMPLEX NUMBERS IN POLAR FORM By the end of this section students will be able to multiply and divide complex numbers in.

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