Free Printable Complex Number

1.

What is the Modulus in a complex number $1\ +\ i\sqrt{3}$

a)

2

b)

4

c)

45 degrees

d)

60 degrees

2.

Find the sum of the complex number (2 + 3i) + (5 - 3i).

a)

7 + 0i

b)

7 + 6i

c)

1 + 11i

d)

11 - i

3.

Which of the following is used to find the product of two Complex Number in rectangular form?

a)

Distributive Property of Multiplication

b)

Multiplying by Complex Conjugate

c)

Combine like terms

d)

LCD

4.

Which of the following determines a directed line segment, or vector, that begins at the origin and ends at that point.

a)

Complex Plane

b)

Cartesian Plane/Rectangular Plane

c)

Polar Coordinate Plane

d)

Imaginary Plane

5.

Find the sum.

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

a)

-2+6i

b)

-35-16i²

c)

12+6i

d)

-35 -16i

6.

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

a)

55 + 48i

b)

73

c)

16 - 6i

d)

55 - 48i

7.

What complex number is represented by the graph?

a)

1+3i

b)

-3-i

c)

-3+i

d)

1 - 3i

8.

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°)

9.

Express in Rectangular form $-5\ \left(\cos120\degree\ +\ i\sin\ 120\degree\right)$

a)

$\frac{−5}{2}+\frac{−5\sqrt{3}}{2}i$

b)

$\frac{5}{2}+\frac{−5\sqrt{3}}{2}i$

c)

$\frac{5}{2}+\frac{5\sqrt{3}}{2}i$

d)

$\frac{−5}{2}+\frac{5\sqrt{3}}{2}i$

10.

$Multiply:\ \ \ \left(2\ cis\ 4\degree\right)\ \ \left(6\ cis\ 100\degree\right)$

a)

$12\ cis\ 104\degree$

b)

$8\ cis\ 104\degree$

c)

$12\ cis\ -96\degree$

d)

$8\ cis\ -96\degree$

11.

$Divide\ :\ \left(2\ cis\ 4\degree\right)\div\ \left(6\ cis\ 100\degree\right)$

a)

$\frac{1}{3}\ cis\ 264\degree$

b)

$\frac{1}{3}\ cis\ -264\degree$

c)

$12\ cis\ 264\degree$

d)

$12\ cis\ -264\degree$

12.

Find the magnitude of z = - 4 + 2i

a)

$2\sqrt{5}$

b)

$-2\sqrt{5}$

c)

$5\sqrt{2}$

d)

$-5\sqrt{2}$

13.

What is the argument of the complex number -4 + 2i.

a)

$206.57\degree$

b)

$2\sqrt{5}$

c)

$5\sqrt{2}$

d)

$26.57\degree$

14.

How many roots does the equation $x^4\ -\ 27\ =\ 0$ ?

a)

0

b)

4

c)

27

d)

x

15.

What is the modulus of the equation $x^5\ =\ 1$

a)

1

b)

5

c)

0 degrees

d)

180 degrees

16.

In the equation $16x^4\ =\ i$ , what are the values of k?

a)

i

b)

4

c)

0, 1, 2, 3, 4

d)

0, 1, 2, 3,

17.

Which of the following enables us to find the powers of a complex number.

a)

De Moivre's Theorem

b)

Complex Roots Theorem

c)

Distributive Property of Multiplication.

d)

Foil Method

18.

$Evaluate:\ \ \left(cis\ 45\degree\right)\ ^4$

a)

-1

b)

1

c)

i

d)

-i

19.

Express 3 - 4i in standard form.

a)

3 - 4i

b)

-3 + 4i

c)

-1

d)

3 + (-4i)

20.

In the Complex Number 4 - 8i, what is the imaginary part?

a)

4

b)

-8

c)

-8i

d)

8i

21.

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

a)

-18

b)

18

c)

-18i

d)

18i

22.

Simplify i²³

a)

i

b)

-i

c)

1

d)

-1

23.

Find the modulus of the complex number. Also state what quadrant the point would land in.

-3 + i

a)

3, Quadrant 3

b)

2, Quadrant 2

c)

√10, Quadrant 3

d)

√10, Quadrant 2

24.

What quadrant would the point in polar form land in?4 ( cos π /3 + i sin π /3).

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

25.

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)

Complex Number

Total questions: 25

Worksheet time: 13mins

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