Polar Complex Numbers

In the complex plane, the ____________ is the distance from the origin to the complex number point z.

The _________________ is the radian or degree measure of the counter clockwise rotation of the vector representing complex number z.

The rectangular form of a complex number is written as z = a + bi, with (a, b) representing the point in the complex plane. Which of the following represent that point as written in polar form?

In the polar equation z = 6 (cos(45^o) + i sin(45^o), the modulus is:

In the polar equation z = 6 (cos(45^o) + i sin(45^o), the argument is:

Express the point in polar form in rectangular form.
4 ( cos π /3 + i sin π /3)

• 2 + 2√3 i

• 2 + √3 i

• 2 - 2√3 i

• -2 + 2√3 i

Find    
5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)
in polar form.  Then express your final answer in rectangular form.

• -10

• 10

• -10i

• 10i

Find
 1/2 ( cos π /3 + i sin π /3)
÷ 3 ( cos π /6 + i sin π /6)
and express your final answer in rectangular form.

• √3/12 + 1/12 i

• 12√3 + 12 i

• √3/12 - 1/12 i

• 12√3 - 12i

Express the complex number in polar form.
6 + 2i

• 6.32 ( cos 0.32 + i sin 0.32)

• 6.32 ( cos 0.45 + i sin 0.45)

• 1.73 ( cos 0.32 + i sin 0.32)

• 1.73 ( cos 0.45 - i sin 0.45)