Free Printable Complex Numbers

1.

Simplify the following radical: √32

a)

3√2

b)

4√8

c)

16√2

d)

4√2

2.

Simplify √-28

a)

-√28

b)

-2i√7

c)

2i√7

d)

28i

3.

Simplify -√-48

a)

4i√3

b)

-4i√3

c)

i√48

d)

-48i

4.

√-36

a)

6

b)

-6

c)

-6i

d)

6i

5.

-3√80a⁷

a)

4a³√5a

b)

-12a³√5a

c)

-3a³√5a

d)

-48a³√5a

6.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

7.

Find the sum.
(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

8.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

9.

Simplify:
-3i(4 + 2i)

a)

6 - 12i

b)

6 + 12i

c)

-12i - 6i²

d)

-12i + 6i²

10.

Simplify:
(2 - 3i)(5 + 4i)

a)

22 - 7i

b)

22 + 7i

c)

22 - 7i²

d)

22 + 7i²

11.

Simplify
(-6 - 2i)²

a)

32

b)

36-4i

c)

36+24i

d)

32+24i

12.

(4-5i)(4+5i)

a)

41

b)

-9

c)

41+40i

d)

-9+40i

13.

Match the following non-real roots with their complex number form: $a\cdot i$ where $a$ is a real number.

a)

$\sqrt[]{-25}$

1.

$5i$

b)

$\sqrt[]{-36}$

2.

$6i$

c)

$\sqrt[]{-100}$

3.

$10i$

d)

$\sqrt[]{-45}$

4.

$3\sqrt[]{5}\cdot i$

e)

$\sqrt[]{-\frac{144}{625}}$

5.

$\frac{12}{25}i$

14.

Which gives the STANDARD FORM for the complex number:

$15-\sqrt[]{-81}$

a)

$15+9i$

b)

$15-8i$

c)

$15-9i$

d)

$15-9\sqrt[]{-1}$

15.

Label the

REAL part __

and the

IMAGINARY part __

of the complex number.

a)

IMAGINARY part

b)

REAL part

1

2

1)

2)

16.

Label the

REAL part __

and the

IMAGINARY part __

of the complex number.

a)

IMAGINARY part

b)

REAL part

1

2

1)

2)

17.

Which gives the STANDARD FORM for the complex number:

$-9+\sqrt[]{-196}$

a)

$-9+14i$

b)

$-9-14i$

c)

$9+14i$

d)

$9-14i$

18.

Match the complex number with its STANDARD FORM:

$a+bi$

a)

$-29+\sqrt[]{-49}$

1.

$-29+7i$

b)

$\frac{2}{5}-\frac{\sqrt[]{-81}}{7}$

2.

$\frac{2}{5}-\frac{9}{7}i$

c)

$-131+\sqrt[]{-441}$

3.

$-131+21i$

d)

$242-\sqrt[]{-289}$

4.

$242-17i$

e)

$114-\sqrt[]{-243}$

5.

$114-9\sqrt[]{3}\cdot i$

19.

Add the two complex numbers:

$\left(-7+16i\right)+\left(-18+13i\right)$

a)

$-23-5i$

b)

$-25-29i$

c)

$-25+29i$

d)

$-11+29i$

20.

Subtract the two complex numbers:

$\left(14+9i\right)-\left(23+11i\right)$

a)

$-9-20i$

b)

$37+20i$

c)

$-9+20i$

d)

$-9-2i$

21.

Add the two complex numbers:

$\left(5+7i\right)+\left(8+3i\right)$

a)

$12+11i$

b)

$13+10i$

c)

$-2+5i$

d)

$13-10i$

22.

Subtract the two complex numbers:

$\left(-26-18i\right)-\left(42-39i\right)$

a)

$-68-21i$

b)

$-68-57i$

c)

$16+21i$

d)

$-68+21i$

23.

Find the Sum

3i + 2i

a)

5i

b)

5i²

c)

6i

d)

-5

24.

Find the sum.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

25.

$-3+6i-\left(-5-3i\right)-8i$

(a)

26.

Simplify:

(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

27.

(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

28.

$4i\left(-2-8i\right)$

(a)

29.

(3+8i)(-2-i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

30.

$\left(1-7i\right)^2$

(a)

31.

Simplify:
(7 + 2i)(9 - 6i)

a)

75-24i

b)

63 - 24i - 12i²

c)

51 - 24i

d)

58 + 60i

32.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

33.

Simplify
√-25

a)

-5i

b)

5

c)

5i

d)

-5

34.

Simplify:
√-108

a)

3i√6

b)

3i√20

c)

6i√3

d)

20i√3

35.

Simplify
2i - 7i + 10

a)

-5i+10

b)

5i

c)

9i+10

d)

5i+10

36.

Simplify
3i - (4 + 7i)

a)

-4 + 10i

b)

21 - 12i

c)

4 - 10i

d)

-4 - 4i

37.

Find the sum.
(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

38.

Multiply
(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

39.

Multiply
(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

40.

Multiply:
(4 – 3i)(7 + 2i)

a)

A. 22 - 13i

b)

B. 28 - 19i

c)

C. 34 - 13i

d)

D. -34 - 29i

41.

i⁷

a)

i

b)

-i

c)

1

d)

-1

42.

i⁶⁶

a)

1

b)

i

c)

-1

d)

-i

43.

i⁵²

a)

i

b)

-i

c)

1

d)

-1

44.

How do you write a complex number?

a)

a-bi

b)

a+bi

c)

ai+b

d)

ai-b

45.

What is the simplified form of (8 -3i)²?

a)

73

b)

16 - 6i

c)

55 + 48i

d)

55 - 48i

46.

What is the simplified form of (-6i)(3i)

a)

-18

b)

-18i

c)

18

d)

-18i²

47.

What complex number is represented by the graph?

a)

-3-i

b)

-3+i

c)

1+3i

d)

1-3i

48.

What complex number is shown on the graph?

a)

(-2,-3)

b)

-2-3i

c)

2-3i

d)

3i-2

49.

Match the expression to the graph shown in the complex plane.

a)

-2i-3i

b)

(0,-5)

c)

-6i

d)

-2(3i)

50.

Match the expression to the graph shown in the complex plane.

a)

(4,0)

b)

4 + 4i

c)

-4(i²)

d)

4i

Complex Numbers

Total questions: 50

Worksheet time: 3hrs 26mins

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