Free Printable Imaginary and Complex Numbers

1.

What is an imaginary number?

a)

A number that cannot be used in mathematical calculations

b)

A complex number that can be written as a real number multiplied by the imaginary unit i.

c)

A number that doesn't exist in the real world

d)

A number with no value

2.

What is a complex number?

a)

A number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit.

b)

A number that can only be expressed in the form a - bi

c)

A number that has no real part

d)

A number that can only be expressed in the form a + bi

3.

Simplify the expression: √(-16)

a)

4i

b)

16

c)

-4

d)

0

4.

What is the value of i^2?

a)

1

b)

2

c)

0

d)

-1

5.

Add (3 + 2i) + (4 - 5i) and write the answer in a + bi form.

a)

9 - 2i

b)

2 - 3i

c)

7 - 3i

d)

5 + 7i

6.

Subtract (5 - 3i) - (2 + 4i) and write the answer in a + bi form.

a)

2 - 7i

b)

4 - 5i

c)

3 - 7i

d)

8 - 1i

7.

Perform the operation (3 + 2i) * (4 - 5i) and write the answer in a + bi form.

a)

15 + 3i

b)

20 - 10i

c)

22 - 7i

d)

12 - 7i

8.

If z = 2 + 3i and w = 4 - 2i, find z + w and write the answer in a + bi form.

a)

6 + i

b)

2 - 5i

c)

10 + 3i

d)

8 - i

9.

If a = 1 + 2i and b = 3 - 4i, find a + b and write the answer in a + bi form.

a)

4 - 2i

b)

2 - 6i

c)

4 - 6i

d)

2 - 2i

10.

What is the value of i^3?

a)

1

b)

i

c)

-1

d)

-i

11.

What is the imaginary part of the complex number: 5 - 6i

a)

5

b)

-6i

12.

Find the real part of the complex number: 7 + 8i

a)

7

b)

8

c)

15

d)

1

13.

What is the square root of -1?

a)

1

b)

i

c)

-1

d)

0

14.

If z = 3 + 4i and w = 1 - 2i, find z + w and write the answer in a + bi form.

a)

4 + 2i

b)

2 + 2i

c)

4 - 2i

d)

2 - 2i

15.

What is the real part of a complex number?

a)

The 'a' in the expression a + bi

b)

The 'b' in the expression a + bi

c)

The 'i' in the expression a + bi

d)

Both 'a' and 'b' in the expression a + bi

16.

Multiply:
(2-5i)(2+5i)

a)

29

b)

4 - 25i

c)

25 - 10i

d)

-21

17.

i⁷⁹

a)

i

b)

1

c)

-1

d)

-i

18.

(2i)(3i)

a)

5i

b)

-5

c)

6i²

d)

-6

19.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

20.

i¹³

a)

-1

b)

1

c)

i

d)

-i

21.

a)

7

b)

-7

c)

7i

d)

-7i

22.

Simplify:
3√-81

a)

-27

b)

3i√3

c)

27i

d)

9i

23.

Fully simplify. $\left(6\sqrt{-7}\right)\left(\sqrt{-3}\right)$

a)

$-6i\sqrt{21}$

b)

$-6\sqrt{21}$

c)

$6\sqrt{21}$

d)

$6i\sqrt{21}$

24.

Write $\sqrt{-200}$ in simplest radical form.

a)

$5\sqrt{-8}$

b)

$5i\sqrt{8}$

c)

$10i\sqrt{2}$

d)

$10\sqrt{-2}$

25.

Write $\sqrt{-10}$ in simplest radical form.

a)

$-i\sqrt{10}$

b)

$i\sqrt{10}$

c)

$-\sqrt{5}\sqrt{2}$

d)

$\sqrt{5}\sqrt{2}\sqrt{-1}$

26.

$-\sqrt{100}+\sqrt{-9}+\sqrt{9}-\sqrt{-16}$

a)

13 +7i

b)

-7 - 7i

c)

13 - i

d)

-7 - i

27.

$\sqrt{144}-\sqrt{-90}+\sqrt{16}+\sqrt{-10}$

a)

$16-2i\sqrt{10}$

b)

$16+4i\sqrt{10}$

c)

$16+3i\sqrt{10}$

d)

$12-2i\sqrt{10}$

Imaginary and Complex Numbers

Total questions: 27

Worksheet time: 41mins

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