Free Printable Complex Quiz

1.

a)

10

b)

-10

c)

10i

d)

-10i

2.

a)

5i

b)

-5i

c)

5+i

d)

-5

3.

What is the complex conjugate of 4-3i?

a)

A. 1/(4-3i)

b)

B. 1/(4+3i)

c)

C. -4 + 3i

d)

D. 4 + 3i

4.

Simplify:
i⁷

a)

i

b)

-i

c)

1

d)

-1

5.

Solve
3x² - 5 = -446

a)

±√-147

b)

7i√3

c)

±7i√3

d)

-7√3

6.

Simplify:
√-108

a)

3i√6

b)

3i√20

c)

6i√3

d)

20i√3

7.

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

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

8.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

9.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

10.

Simplify
(-6 - 2i)²

a)

32

b)

36-4i

c)

36+24i

d)

32+24i

11.

a)

A.

b)

B.

c)

C.

d)

D.

12.

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

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

13.

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

a)

75-24i

b)

63 - 24i - 12i²

c)

51 - 24i

d)

58 + 60i

14.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

15.

Simplify
√-25

a)

-5i

b)

5

c)

5i

d)

-5

16.

Simplify:
3√-81

a)

-27

b)

3i√3

c)

27i

d)

9i

17.

What is the conjugate of -2+5i?

a)

-5+2i

b)

-2-5i

c)

2+5i

d)

5-2i

18.

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

a)

1-i

b)

1+i

c)

10+10i

d)

1+10i

19.

What complex number is represented by the graph?

a)

-3-i

b)

-3+i

c)

1+3i

d)

1-3i

20.

Which are possible coordinates of the point graphed?

a)

(-2, 120^o)

b)

(-2, 60^o)

c)

(2, -120^o)

d)

(2, 60^o)

21.

Convert the rectangular coordinate (0, -3) to polar coordinates.

a)

(3, -270^o)

b)

(3, 270^o)

c)

(-3, 270^o)

d)

Not Possible

22.

The rectangular form of the complex number 12(cos315^o + i sin315^o) is...

a)

6√2 + 6√2 i

b)

6√2 - 6√2 i

c)

-6√2 + 6√2 i

d)

-6√2 - 6√2 i

23.

The product of the following complex number in polar form √5(cos130^o + i sin130^o) ⋅ √45(cos15^o + i sin15^o) is...

a)

50(cos145^o + i sin145^o)

b)

15(cos145^o + i sin145^o)

c)

81(cos100^o + i sin100^o)

d)

All Options are Correct

24.

Let w=-√3/2 + 1/2 i calculate the modulus and argument.

a)

3, 120^o

b)

5, 270^o

c)

1, 150^o

d)

Not Possible

25.

If z=√2+√2 i then arg(z²)=

a)

0^o

b)

60^o

c)

90^o

d)

Not Possible

26.

Where is point B located?

a)

2 + i

b)

-3

c)

2i

d)

-1 - i

27.

Where is point A located?

a)

2 + i

b)

-3

c)

2i

d)

-1 - i

28.

(-7 + 9i) + (2 - 10i)

a)

-5 + i

b)

-5 - i

c)

-9 + 1

d)

9 - i

29.

Choose the correct answer for the operation pictured.

a)

7-13i

b)

7-i

c)

1-13i

d)

1-i

30.

Simplify

a)

(-10+6i)/17

b)

(1+50i)/61

c)

(-23+36i)/25

d)

(-21+33i)/34

31.

(-5 + 10i)(-5 - 10i) = 125

a)

True

b)

False

32.

a)

A

b)

B

c)

C

d)

D

33.

a)

A

b)

B

c)

C

d)

D

34.

Simplify.

a)

b)

c)

d)

35.

Simplify.

a)

b)

c)

d)

36.

Simplify.

a)

b)

c)

d)

37.

Simplify

a)

9i/5

b)

2i

c)

8i/5

d)

13i/5

38.

Simplify

a)

(-7-3i)/10

b)

(-4-3i)/7

c)

6i/7

d)

(4i-3)/7

39.

Simplify

a)

17i

b)

15i

c)

4i-10

d)

2i-10

40.

Simplify

a)

(-10+6i)/17

b)

(-8+15i)/17

c)

(-23+36i)/25

d)

(-21+33i)/34

41.

What is the conjugate of $-4-10\sqrt{7}$

a)

$-4+10\sqrt{7}$

b)

$4+10\sqrt{7}$

c)

$4-10\sqrt{7}$

42.

What is the conjugate of $-5+\sqrt{2}$

a)

$-5-\sqrt{2}$

b)

$5-\sqrt{2}$

c)

$5+\sqrt{2}$

43.

What is the conjugate you would multiply by?

a)

5+2i

b)

5-2i

c)

-5-2i

d)

-5+2i

44.

What is the conjugate you would multiply by?

a)

2+i

b)

2-i

c)

-2+i

d)

-2-i

45.

What is the denominator after multiplying and before simplifying?

a)

17

b)

13

c)

5i

d)

15i

46.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.

a)

-3+5i

b)

-3-5i

c)

-5i

d)

3-5i

47.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that -7i is a root.

a)

7i

b)

-7i+1

c)

1-7i

d)

1+7i

48.

All imaginary roots comes in pairs.

a)

True

b)

False

49.

Convert the rectangular coordinates to polar form

a)

(√2 , 7π/4)

b)

(2 , 3π/4)

c)

(4 , π/4)

d)

(4 , 5π/4)

50.

Convert the polar coordinates to rectangular form

a)

(1, 1)

b)

(1, -1)

c)

(-1, 0)

d)

(-1, -1)

51.

Convert the polar coordinates to rectangular form

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

52.

Which equation represents the polar graph?

a)

r = sin θ

b)

r = sin 4θ

c)

r = 4 sin θ

d)

r = 4 cos θ

53.

Convert the polar coordinates to rectangular form $\left(\sqrt{2},\ -\frac{\pi}{4}\right)$

a)

(1, 1)

b)

(1, -1)

c)

(-1, 0)

d)

(-1, -1)

54.

Convert the polar coordinates to rectangular form $\left(6,\ \frac{2\pi}{3}\right)$

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

55.

Which point represents (3, 3π/4)?

a)

F

b)

E

c)

B

d)

A

56.

How do you write an ordered pair?

a)

(X,X)

b)

(θ, r)

c)

(r,θ)

d)

(Y,Y)

57.

Which point represents (-4, 4π/3)

a)

F

b)

E

c)

B

d)

A

58.

Are the roots of the function f(x)=3x²+3x+3 real or imaginary? (hint: graph it)

a)

Real Roots

b)

Imaginary Roots

c)

Impossible to tell

d)

Both

59.

$Write\ \frac{7-3i}{5-2i}$ as a single complex number.

a)

$\frac{7}{5}+\frac{3}{2}i$

b)

$\frac{41}{29}-\frac{1}{29}i$

c)

$1-\frac{1}{29}i$

d)

$\frac{41}{29}-i$

60.

Which of the following would be a root with 3i?

a)

3i²

b)

-3i

c)

3i

d)

-3i²

61.

If a+bi is a root of a polynomial, then _______ is also a root.

a)

i²

b)

a-bi

c)

a+bi

d)

-i²

62.

Express $\sqrt{-300}$ in terms of $i$

a)

$10\sqrt{3}$

b)

$i\sqrt{300}$

c)

$10i\sqrt{3}$

d)

$-\sqrt{300}$

63.

Solve the equation $x^2+8x+20=0$

a)

$-4\pm2i$

b)

$2i\pm4$

c)

$-2\pm4i$

d)

$3\pm2i$

64.

Find the complex conjugate of $1-i\sqrt{2}$

a)

$i\sqrt{2}+1$

b)

$1+i\sqrt{2}$

c)

$2+i\sqrt{1}$

d)

$1+\sqrt{2}$

65.

Which of the following would be a root with 3i?

a)

3i²

b)

-3i

c)

3i

d)

-3i²

66.

How many complex roots (real or imaginary) of x² + 2x + 1?

a)

1

b)

2

c)

3

d)

4

67.

A complex number is denoted by______.

a)

C

b)

Z

c)

R

d)

z

68.

The argument of the product of two complex numbers is the _______ of the arguments of the complex numbers

a)

sum

b)

product

c)

inverse

d)

conjugate

69.

In polar coordinates, r is the ________.

a)

argument

b)

modulus

c)

diameter

d)

angle

70.

A function which is analytic everywhere in the finite plane is called _______.

a)

entire function

b)

analytic function

c)

differentiation

d)

continuous function

71.

$e^z$ is not defined in $z=\infty$ then the function is ________

a)

harmonic function

b)

continuous function

c)

entire function

d)

analytic function

72.

Suppose f(z) is analytic in a domain, if its real part is a constant then f(z) is

a)

a continuous function

b)

a harmonic function

c)

an analytic function

d)

a constant function

73.

Absolute value of $\frac{\left(1+3i\right)\left(1-2i\right)}{3+4i}$ is ............

a)

2

b)

$\sqrt{3}$

c)

$\sqrt{2}$

d)

3

74.

f(z)= sin x cos hy + i cos x sin hy is differential at every point.

a)

true

b)

false

75.

Let z=x+iy then z is real iff z= …….

a)

x

b)

y

c)

z

d)

z̅

76.

If f is continuous at z₀ then ………… are continuous at z₀

a)

│f│

b)

Re f

c)

Im f

d)

all the above

77.

For f(z)= sin z, z=0 is a zero of order …………..

a)

1

b)

$\frac{\pi}{2}$

c)

0

d)

-1

78.

Every real number is

a)

a positive number

b)

a rational number

c)

a complex number

d)

a negative number

79.

In z = a + bi, if i is replaced by -i, then another complex number obtained is said to be

a)

additive inverse of z

b)

prime factor of z

c)

complex conjugate of z

d)

multiplicative inverse of z

80.

i¹⁰ is equal to

a)

-1

b)

i

c)

1

d)

0

81.

The polar coordinate representation of the complex number

z=x+iy\

is -----

a)

$z=re^{i\theta}$

b)

$z=re^{-i\theta}$

c)

$z=\frac{1}{r}e^{i\theta}$

d)

$z=\frac{1}{re^{i\theta}}$

82.

The argument of the complex number

z=2+4i

is ----

a)

$\tan\left(\frac{1}{2}\right)$

b)

$\tan^{-1}\left(\frac{1}{2}\right)$

c)

$\tan^{-1}\left(2\right)$

d)

$\tan\left(2\right)$

83.

$z=r\cos\theta+ir\sin\theta$ is known as -----

a)

trigonometric form

b)

exponential form

c)

polar form

d)

all the above

84.

$z-\ \overline{z}\ =\ ---$

a)

$2iRe\left(z\right)$

b)

$2Re\left(z\right)$

c)

$2iIm\left(z\right)$

d)

$2Im\left(z\right)$

85.

Modulus of the complex number

z=4-5i

is ------

a)

$\sqrt{41}$

b)

$41$

c)

$\sqrt{9}$

d)

$9$

86.

what was the name of mathematicians who firstly had used the number i

a)

EULER

b)

GAUSS

c)

DESCARTES

d)

TEACHER

Complex Quiz

Total questions: 86

Worksheet time: 5hrs 9mins

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