Complex Numbers

by Meg Cohrs

| 22 Questions1

1

Given the general form of a complex number, a+bi, (1) what is considered the real part of the complex number and (2) what is considered the imaginary part?

2

1

Given 3+4i, (1) what is the real part and (2) what is the imaginary part of the complex number?

3

1

Given 5+34i, (1) what is the imaginary part and (2) what is the real part of the complex number?

4

1

Given 15+i, (1) what is the real part and (2) what is the imaginary part of the complex number?

5

1

i²=

1

-1

i

-i

6

1

i³=

1

-1

i

-i

7

1

i4=

1

-1

i

-i

8

1

i5=

1

-1

i

-i

9

1

Simplify 4i2+2i+13.

-4+2i+13

9+2i

17+2i

19i

10

1

Explain your process in simplifying the expression in Question 9.

11

1

Multiply (2+3i)(4+6i) and show the product in simpliest form.

18i2+24i+8

8+18i2

-10+24i

6+9i

12

1

Explain your process in multiplying and reducing in Question 11.

13

1

Multiply the two complex numbers (2-5i2)(7+3i) and show the product in simpliest form.

-11-29i

-5i-2i3

-5i+3i-5i2

14-15i3

14

1

The conjugate of 5+8i is 5+8i.

True

False

15

1

The conjugate of a complex number involves the same real and imaginary part but changes the sign between them.

True

False

16

1

These two complex numbers are conjugates: (3+8i) and (3-8i).

True

False

17

1

The conjugate of 1+6i is 6+1i.

True

False

18

1

The conjugate of 4+i is _______.

19

1

What is the modulus if z= 7+9i. (Reduce to the simplest form)

|z|= 4

|z|= 3+ √7

|z|= √130

|z|= √63

20

1

Explain what steps you went through in Question 19 to find the modulus.

21

1

Use what we know about conjugates to simplify the following: (1+4i)/(9-5i)

10+i

29

9i/8

(-11+41i)/106

22

1

Explain how you simplified the expression in Question 21.

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