11.2 Geometric Representations of Complex Numbers.

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Presentation transcript:

11.2 Geometric Representations of Complex Numbers

Graphing Complex Numbers In Algebra 2, you learned how to graph a complex number… Real Part Imaginary Part

Graphing Complex Numbers Graph the point 5 - 7i

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(  )

Covert each complex number to polar form:

Covert each complex number to rectangular form:

Products of Complex Numbers Back in Algebra 2, you learned how to multiply complex numbers… Foil This

Products of Complex Numbers in Polar Form Let’s multiply 2 complex numbers: Reorder the terms…

Products of Complex Numbers in Polar Form Reorder the terms…

Products of Complex Numbers in Polar Form Translation: When you multiply complex numbers in polar form, you simply multiply the radii & add the angles.

Multiply using the polar form of the complex number: