Free Printable Unit 4 Test Review

1.

What is theta of $\tan\theta=\frac{-\ \sqrt[]{3}}{3}$

Select all that apply.

a)

$\frac{5\pi}{6}$

b)

$\frac{\pi}{6}$

c)

$\frac{7\pi}{6}$

d)

$\frac{11\pi}{6}$

2.

From the graph, what is the equation of the complex number?

a)

z=-3+2i

b)

z=3+2i

c)

z=3-2i

d)

z=2+3i

3.

From the graph, what is the equation of the complex number?

a)

z=1+2i

b)

z=-1+2i

c)

z=1-2i

d)

z=-1-2i

4.

From the graph, what is the equation of the complex number?

a)

z=-2+4i

b)

z=-2-4i

c)

z=2-4i

d)

z=2+4i

5.

Which graph represents the complex number below:

z=-2i

a)

b)

c)

d)

6.

What is the conjugate of z=3-2i?

a)

2-3i

b)

-3+2i

c)

-3-2i

d)

3+2i

7.

What is the conjugate of z=-i

a)

-1

b)

1

c)

i

d)

None

8.

What is the conjugate of z=-2+5i

a)

2+5i

b)

-2-5i

c)

-2+5i

d)

2-5i

9.

What is the value of $\tan\theta=UND$ ?

Select all that apply.

a)

$\pi$

b)

$\frac{\pi}{2}$

c)

$\frac{3\pi}{2}$

d)

$2\pi$

10.

Given that $z_1=2-i\$ and $z_2=1+4i$ . What is $z_1+z_2$ ?

a)

-3+3i

b)

1+3i

c)

3+3i

d)

None

11.

Given that $z_1=-i\$ and $z_2=-3+2i$ . What is $z_1-z_2$ ?

a)

3-3i

b)

3+i

c)

-3-3i

d)

None

12.

Given that $z_1=3-i$ and $z_2=3+i$ . What is $z_1z_2$ ?

a)

9

b)

10

c)

8

d)

None

13.

Given that $z_1=2-i$ and $z_2=1+3i$ . What is $z_1z_2$ ?

a)

-1+5i

b)

5+4i

c)

5+5i

d)

None

14.

Find the modulus of $z=-3i$

a)

3

b)

-3

c)

9

d)

None

15.

Find the modulus of $z=1+\sqrt[]{3}i$

a)

-2

b)

4

c)

2

d)

None

16.

Find the modulus of $z=-4+3i$

a)

25

b)

5

c)

-5

d)

None

17.

When multiplying a complex number by its conjugate, the result will always be an imaginary number.

a)

Sometimes

b)

Always

c)

Never

18.

Write the complex number in polar form.

$z=1+\sqrt[]{3}i$

a)

$z=2\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right)$

b)

$z=2\left(\cos\frac{5\pi}{3}+i\sin\frac{5\pi}{3}\right)$

c)

$z=2\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right)$

d)

$z=2\left(\cos\frac{11\pi}{6}+i\sin\frac{11\pi}{6}\right)$

19.

Write the complex number in polar form.

$z=-2i$

a)

$2\left(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2}\right)$

b)

$z=2\left(\cos\pi+i\sin\pi\right)$

c)

$z=2\left(\cos\left(0\pi\right)+i\sin\left(0\pi\right)\right)$

d)

$z=2\left(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}\right)$

20.

Find the indicated power using DeMoivre's Theorem.

$\left(1+i\right)^6$

Leave your answer in polar form.

a)

$\sqrt[]{2}\left(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2}\right)$

b)

$8\left(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}\right)$

c)

$8\left(\cos\frac{\pi}{4}+i\sin\frac{\pi}{4}\right)$

d)

$8\left(\cos\left(\frac{3\pi}{2}\right)+i\sin\left(\frac{3\pi}{2}\right)\right)$

21.

Find the indicated power using DeMoivre's Theorem.

$\left(z=-3+3\ \sqrt[]{3}i\right)^9$

a)

$6^9\left(\cos\pi+i\sin\pi\right)$

b)

$6^6\left(\cos2\pi+i\sin2\pi\right)$

c)

$6^9\left(\cos2\pi+i\sin2\pi\right)$

d)

None

22.

Find the quotient $\frac{z_1}{z_2}$ of

$z_1=2\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right)$ and $z_2=\cos\left(\frac{\pi}{6}\right)+i\sin\left(\frac{\pi}{6}\right)$

a)

$z_2=2\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right)$

b)

$z_2=2\cos\left(\frac{\pi}{6}\right)+i\sin\left(\frac{\pi}{6}\right)$

c)

$z_2=\frac{1}{2}\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right)$

d)

None

23.

Find the square roots of $z=64i$ .

Select all that apply.

a)

$8\left(\cos\frac{5\pi}{4}+i\sin\frac{5\pi}{4}\right)$

b)

$8\left(\cos\frac{\pi}{4}+i\sin\frac{\pi}{4}\right)$

c)

$8\left(\cos\frac{7\pi}{4}+i\sin\frac{7\pi}{4}\right)$

d)

$8\left(\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4}\right)$

24.

Given $z=2+6i$ . Which of the following is a NOT true statement?

a)

The real part is 2 and the imaginary part is 6.

b)

The conjugate is

2-6i

c)

The modulus is $2\ \sqrt[]{10}$

d)

All of these statements are correct

25.

Which of the following matches the graph?

a)

{z l $1<\left|z\right|<3\$ }

b)

{z l $1<\left|z\right|\le3$ }

c)

{z l $1\le\left|z\right|\le3$ }

d)

{z l $-3<\left|z\right|\le1$ }

Unit 4 Test Review

Total questions: 25

Worksheet time: 42mins

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