Polar Form of Complex Numbers

Question 1

If z = 13 – 7i, what is the value of |z|?

Revolt · Accepted Answer

StartRoot 218 EndRoot

Question 2

Review the four points shown on the polar coordinate system.

Revolt · Accepted Answer

point A

Question 3

Review the graph of complex number z.

Revolt · Accepted Answer

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (5, negative 2).

Question 4

Review the graph of complex number z.

Revolt · Accepted Answer

StartRoot 10 EndRoot

Question 5

Which pair of equations can be used to verify the rectangular form, z = a + bi, and the polar form of a complex number are equivalent?

Revolt · Accepted Answer

a = rcos(θ) and b = rsin(θ)

Question 6

Which graph represents –4 + 3i?

Revolt · Accepted Answer

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is at (negative 4, 3).

Question 7

What is the polar form of ?

Revolt · Accepted Answer

4 StartRoot 3 EndRoot (cosine (StartFraction 4 pi Over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Question 8

What is the rectangular form of 17(cos(315°) + isin(315°))?

Revolt · Accepted Answer

StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction minus StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction i

Question 9

Convert the polar coordinates (5, 6.1) to rectangular coordinates.

Revolt · Accepted Answer

(4.92, –0.91)

Question 10

What is the argument of z = ?

Revolt · Accepted Answer

Negative StartFraction pi Over 3 EndFraction

Polar Form of Complex Numbers Answers