Free Printable Solving Equations and Expressions

1.

Which of the following is equivalent to the value of x?

x = (1234)(134)(1432)

a)

(124)

b)

(1342)

c)

(1243)

d)

(123)

e)

iota

2.

Which of the following is equivalent to x?
$x=\left(12345\right)^{10}\left(1234\right)^{12}$

a)

iota

b)

(1245)

c)

(12435)

d)

(12354)

e)

(15234)

3.

Which of the following is equivalent to the value of x?

$x\ =\ \left(123456\right)^{-1}$

a)

does not exist

b)

(165432)

c)

iota

d)

(165234)

e)

(123465)

4.

Solve the equation

(123)(x) = (1243)

(a)

5.

Solve the equation

(x)(1234) = (124)

(a)

6.

z1 = 4+2i

z2 = -1 + 3i

Which of the following are true?

a)

z1*z2 is in the first quadrant

b)

z1+z2 is in the first quadrant

c)

z1-z2 is in the first quadrant

d)

z1/z2 is in the first quadrant

e)

(z1)^2 is in the first quadrant.

7.

Which of the following statements are true about the complex numbers shown in the complex plane?

a)

The absolute value of each complex number are equal

b)

The product of the red and green is a real number

c)

The product of the red and blue is a real number

d)

The product of the red and yellow is a real number.

e)

The product of all the complex numbers shown is a real number

8.

What is the red complex number written in it's polar form?

(a)

9.

Which of the following is equivalent to z?

$z\ =\ \left(2+5i\right)^2$

a)

-21+20i

b)

5.4cis(136)

c)

29cis(136)

d)

28cis(68)

e)

i + j + k

10.

What is the blue complex number * green complex number?

(a)

11.

Which of the following statements are true?

a)

blue = 3.1 + 8.8i

b)

green = -3 = -3cis(180)

c)

yellow = 5cis(340)

d)

red = 6i=6cis(90)

12.

Which of the following are solutions of the equation?

$z^8=1$

a)

1 and cis(180)

b)

cis(45) and i

c)

cis(145) and cis(225)

d)

-1 and -i

e)

cis(315) and cis(0)

13.

Which of the following values solves the equation?

$z^3=cis\left(66\right)$

a)

cis(22)

b)

cis(66)

c)

cis(146)

d)

cis(266)

e)

cis(26)

14.

A red quaternion and a green quaternion are shown from two different perspectives in their complex planes.

Which of the following when added together is equivalent to |red|+|green|?

a)

$\sqrt[]{42}$

b)

$\sqrt[]{17}$

c)

$\sqrt[]{15}$

d)

$4$

e)

$\sqrt[]{13}$

15.

A red quaternion and a green quaternion are shown from two different perspectives in their complex planes.

What is green x red?

(a)

16.

A red quaternion and a green quaternion are shown from two different perspectives in their complex planes.

What is green/2k?

(a)

17.

If (i + j)z + 2i + k = 3i + 2k, then z = ?

(a)

18.

How many roots of f(z) are on the red domain?

$f\left(z\right)\ =\ z^2+16$

a)

0

b)

1

c)

2

d)

3

19.

How many roots of f(z) are on the blue domain?

$f\left(z\right)\ =\ z^2+16$

a)

0

b)

1

c)

2

d)

3

20.

How many roots of f(z) are on the green domain?

$f\left(z\right)\ =\ z^2+16$

a)

0

b)

1

c)

2

d)

3

21.

Which of the following are roots of f(z) given the domain?

a)

5

b)

5i

c)

4i

d)

1+2i

e)

1+3i

22.

Which of the following forms an Algebra?

a)

S = {0, 1, 2, 3, 4} mod 5 wrt +

b)

S = {1, 3, 5} mod 7 wrt *

c)

S = {iota, (123), (132)}

d)

S = {0, 1, i, 1+i} mod 2 wrt +

Solving Equations and Expressions

Total questions: 22

Worksheet time: 17mins

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