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Applying Properties of Operations on Complex Numbers to Solve Problems

Total questions: 15

Worksheet time: 15mins

Name
Class
Date
1.

If z=√2+√2 i then arg(z2)=

a)

0o

b)

60o

c)

90o

d)

Not Possible

2.

Add. Write answer in the form a + bi:

(2+3i)+(52i)\left(-2+3i\right)+\left(5-2i\right)  

(a)  

3.
a)

A

b)

B

c)

C

d)

D

4.

(3 - 2i)*(5 + 4i) - (3+2i)*(5+4i)

a)

-16 - 20i

b)

16 - 20i

c)

0

d)

30 + 24i

e)

non of the above

5.

The complex numbers u and v satisfy the equations u + 2v = 2i and iu + v = 3. Solve the equations for u and v, giving both answers in the form x + iy, where x and y are real.

a)

u = -2 - 2i

v = 1 + 2i

b)

u = 2 + 2i

v = 1 - 2i

c)

u = 2i - 2

v = -1 - 2i

d)

u = 1 + 2i

v = - (2 + 2i)

6.

Solve the equation (2 + 3i)x = (4 - 5i) for x.

a)

x = (4 + 5i) / (2 + 3i)

b)

x = (4 - 5i) / (2 - 3i)

c)

x = (4 - 5i) / (2 + 3i)

d)

x = (4 + 5i) / (2 - 3i)

7.

The product of (3 -2i) and (7+6i) is

a)

21 - 12i

b)

9 + 4i

c)

33 + 4i

d)

21 + 16i

8.

Let w1= 4 - 2i, w2 = -3 + 4i, and w3= 2 + 6i. Which of the following is equal to w1w2 - w3 ?

a)

-2 + 28i

b)

-4 + 22i

c)

-6 +28i

d)

-6 + 16i

e)

-2 +16i

9.

What is the product of (2 + 3i) and (4 - 5i)?

a)

Charlotte thinks it's -23 + 2i

b)

Mia thinks it's 23 + 2i

c)

Evelyn thinks it's -23 - 2i

d)

No one thinks it's 23 - 2i

10.

Calculate the product of (-2 + 3i) and (-1 - 4i).

a)

-14 - 5i

b)

14 - 5i

c)

14 + 5i

d)

-14 + 5i

11.

Find the product of (-2 + 3i) and (1 - 4i).

a)

-2 - 11i

b)

-5 + 8i

c)

7 - 8i

d)

5 - 2i

12.

Simplify: (1 + 7i) * (9 + 3i) - 4 - 2i

a)

-16 + 64i

b)

-16 - 64i

c)

16 - 64i

d)

16 + 64i

13.

Find the product of (-2 + 7i) and (1 - 3i).

a)

-19 + 13i

b)

19 - 13i

c)

-19 - 13i

d)

19 + 13i

14.
a)

A

b)

B

c)

C

d)

D

15.
a)

A

b)

B

c)

C

d)

D