Complex Numbers II - Ambitious

Question 1: If

(x + y) + (x - y) = 5 + 3 i

, find

x

and

y

A

x = 3, y = 2

B

x = 4, y = 1

C

x = 2, y = 0

D

x = 5, y = 3

Question 2: Express

z = 6 + 8 i

in the polar form

A

z = 10 (\cos 53.13 ° + i \sin 53.13 °)

B

z = 14 (\cos 36.87 ° + i \sin 36.87 °)

C

z = 10 (\cos 36.87 ° + i \sin 36.87 °)

D

z = 10 (\sin 53.13 ° + i \cos 53.13 °)

Question 3: Express

z = 4 + 3 i

in the shortened polar form

A

z = 7 36.87 °

B

z = 4 36.87 °

C

z = 5 53.13 °

D

z = 5 36.87 °

Question 4: Express

z = - 4 - 5 i

in the shortened polar form

A

z = 9 51.34 °

B

z = \sqrt{41} 51.34 °

C

z = \sqrt{41} 231.34 °

D

z = 6 231.34 °

Question 5: Express

3 (\cos 15 ° + i \sin 15 °)

in the form

a + i b

A

2.898 + 0.777 i

B

3 + i

C

0.551 + 0.289 i

D

1.457 - 2.721 i

Test: Complex Numbers II - Ambitious