Complex Numbers

Question 1

A complex number is a number in the form

Answer 1

x + yi

Question 2

x is a real number called the

Answer 2

real part

Question 3

y in a complex number is the

Answer 3

imaginary part

Question 4

i = √-1 is called an

Answer 4

imaginary number

Question 5

3 + 5i
real part = ?, imaginary part = ?

Answer 5

real part = 3, imaginary part = 5i

Question 6

In 4i, determine the real part and imaginary part.

Answer 6

real part = 0, imaginary part = 4i

Question 7

Determine the real and imaginary part of 7.

Answer 7

real part = 7, imaginary part = 0

Question 8

i⁰ =

Answer 8

1

Question 9

i¹ is equal to

Answer 9

i

Question 10

i² =

Answer 10

-1

Question 11

i³ =

Answer 11

-i

Question 12

i⁴ =

Answer 12

1

Question 13

Simplify: i²⁰¹⁷ + 2i²⁰¹⁸ - 3i²⁰²⁰

Answer 13

-5 + i

Question 14

Determine the values of x and y in the complex number 2( x + iy ) = 6 - i3.

Answer 14

x = 3, y = - 3/2

Question 15

Operations of Complex Numbers in Algebraic Form
( 5 + 2i ) - ( 4 - 3i) = ?

Answer 15

1 + 5i

Question 16

Operations of Complex Numbers in Algebraic Form
( 3 + 2i ) ( 2 - 5i) = ?

Answer 16

16 - 11i

Question 17

Operations of Complex Numbers in Algebraic Form
( 4 - 2i )/( 3 + 2i ) = ?

Answer 17

8/13 - 14i/13

Question 18

Complex Number in Trigonometric Form
x + iy = ?

Answer 18

r( cosθ + isinθ ) or rcisθ

Question 19

Complex Number in Polar Form
x + iy = ?

Answer 19

r∠θ

Question 20

Absolute value or modulus of the complex number

Answer 20

r = √(x² +y²)

Question 21

Argument or amplitude of the complex number

Answer 21

θ = arctan y/x

Question 22

Express 3 + 4i in trigonometric form.

Answer 22

5( cos53.13° + isin53.13° )

Question 23

Express 2( cos30° + isin30° ) in algebraic/rectangular form.

Answer 23

√3 + i

Question 24

Multiply ( 3cis20° ) ( 2cis40° ) in trigonometric form.

Answer 24

6 ( cos60° + isin60°)

Question 25

Divide 6angle60°/2angle20°.

Answer 25

3angle40°

Question 26

Evaluate ( 1 + i )⁵ and express the answer in x + yi.

Answer 26

-4( 1 + i )

Question 27

Find the 3 cube roots of -1 + i√3.

Answer 27

1st root = cube root of 2 angle 40°
2nd root = cube root of 2 angle 160°
3rd root = cube root of 2 angle 280° or cube root of 2 angle( -80° )

Question 28

What is the product of the complex numbers 3 - 4i and 8e^i53.13°?

Answer 28

40

Question 29

Evaluate ln( 3 + 4i ) in rectangular form.

Answer 29

1.609 + 0.927i

Question 30

Complex Number in Exponential Form

Answer 30

re^iθ