Free Printable Converting Complex Numbers to Polar Form

1.

Write the complex number in polar form

a)

√50 (cos π/2 + i sin π/2)

b)

50 (cos π/4 + i sin π/4)

c)

√50 (cos 5π/4 + i sin 5π/4)

d)

√50 (cos π/4 + i sin π/4)

2.

Write the complex number in polar form

a)

3 ( cos 3π/2 + i sin 3π/2)

b)

3 ( cos π/2 + i sin π/2)

c)

9 ( cos 3π/2 + i sin 3π/2)

d)

3 ( cos 2π + i 2π)

3.

Convert to polar form

a)

A

b)

B

c)

C

d)

D

4.

Calculate the modulus (R) and argument (θ) for z = -5 + 3i Give the argument between -π < θ < π.

a)

R = 5.83, θ = 0.54 rad or 31°

b)

R = 34, θ = 2.6 rad or 149°

c)

R = 5.83, θ = 3.7 rad or 211°

d)

R = 5.83, θ = 2.6 rad or 149°

5.

Identify the rectangular form, modulus, and argument of the complex number represented on the graph.

a)

Rectangular form:

𝑧 = −7i,

Modulus: -7,

Argument: $\pi$

b)

Rectangular form:

𝑧 = −7,

Modulus: 7,

Argument: $\pi$

c)

Rectangular form:

𝑧 = −7+7i,

Modulus: 7,

Argument: $\frac{\pi}{2}$

d)

Rectangular form:

𝑧 = 7i,

Modulus: 7,

Argument: $2\pi$

6.

Find the trigonometric form of the complex number: z = √2 - √6i

a)

z = √8(cos(-60^o) + isin(-60^o))

b)

z = √8(cos(30^o) + isin(30^o))

c)

z = √8(cos(-120^o) + isin(-120^o))

d)

z = √8(cos(60^o) + isin(60^o))

7.

Which of the following complex numbers is in polar form? Select all that apply.

a)

5 + 3i

b)

8 cis 44

c)

10 cis 72

d)

-3 + 2i

8.

Write the complex number in trig form r(cosθ+i sinθ)

a)

4(cos 270 + i sin 270)

b)

4 (cos 0 + i sin 0)

c)

4 (cos 90 + i sin 90)

d)

4 (cos 180 + i sin 180)

9.

What is the polar form of the complex number $z = 0 + i$ ?

a)

$1\text{cis}(\frac{\pi}{2})$

b)

$1\text{cis}(\pi)$

c)

$1\text{cis}(\frac{3\pi}{2})$

d)

$1\text{cis}(2\pi)$

10.

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.

a)

-10

b)

10

c)

-10i

d)

10i

11.

Write the complex number in Polar Form. Express the argument in Degrees: 6+0i

a)

6(cos 270° + i sin 270°)

b)

6(cos 180° + i sin 180°)

c)

6(cos 0° + i sin 0°)

d)

6(cos 90° + i sin 90°)

12.

Convert the complex number to polar

a)

A

b)

B

c)

C

d)

D

13.

Write the complex number - 3i in polar form.

a)

3 ( cos 3π/2 + i sin 3π/2)

b)

9 ( cos 3π/2 + i sin 3π/2)

c)

3 ( cos π/2 + i sin π/2)

d)

3 ( cos 3π/2 - i sin 3π/2)

14.

Calculate the modulus (R) and argument (θ) for z = 4 + 9i. Give the argument between -π < θ < π.

a)

R = 9.05, θ = 1.99 rad or 114°

b)

R = 9.8, θ = 1.2 rad or 66°

c)

R = 97, θ = 1.2 rad or 66°

d)

R = 9.8, θ = 5.13 rad or 294°

15.

$Z=3cis\left(\frac{\pi}{6}\right)$ is written in _________.

a)

POLAR FORM

b)

RECTANGULAR FORM

16.

a)

A

b)

B

c)

C

d)

D

17.

Write the following vector in trigonometric form.

$v=<-5,5>$

a)

$5<\cos135^{\circ},\sin135^{\circ}>$

b)

$5<\cos-45^{\circ},\sin-45^{\circ}>$

c)

$5\sqrt{2}<\cos135^{\circ},\sin135^{\circ}>$

d)

$5\sqrt{2}<\cos45^{\circ},\sin45^{\circ}>$

18.

When a complex number is drawn on the complex plane. The distance from the origin is the value of

a)

the argument

b)

The modulus

c)

The real co-efficient

d)

The imaginary co-efficient

19.

For the number 2-3i the argument measured in degrees would be

a)

between 0 and 90°

b)

between 0 and -90°

c)

between 90° and 180°

d)

between -90° and -180°

20.

For the number 3+4i the argument measured in degrees would be

a)

between 0 and 90°

b)

between 0 and -90°

c)

between 90° and 180°

d)

between -90° and -180°

Converting Complex Numbers to Polar Form

Total questions: 20

Worksheet time: 20mins

Similar Resources on Wayground