Complex Numbers III - Ambitious

Question 1: Write the modified polar form of

z = 3 (\cos 240 ° + i \sin 240 °)

using the shorthand notation

A

z = 3 120 °

B

z = 3 120 °

C

z = 3 240 °

D

z = 3 240 °

Question 2: Write the proper polar form

z = 2 (\cos 25 ° - i \sin 25 °)

using the shorthand notation

A

3 25 °

B

2 335 °

C

3 - 25 °

D

- 3 25 °

Question 3: Multiply the following:

z_{1} = x (\cos θ + i \sin θ)

and

z_{2} = y (\cos φ + i \sin φ)

A

z_{1} z_{2} = x y (\cos (θ + φ) + i \sin (θ + φ))

B

z_{1} z_{2} = x y (\cos (θ + φ) - i \sin (θ + φ))

C

z_{1} z_{2} = (x + y) (\cos (θ + φ) + i \sin (θ + φ))

D

z_{1} z_{2} = x y (\cos (θ φ) + i \sin (θ φ))

Question 4: Find

z_{1} z_{2}

, where

z_{1} = 3 (\cos 15 ° + i \sin 15 °)

and

z_{2} = 5 (\cos 63 ° + i \sin 63 °)

A

z_{1} z_{2} = 15 (\cos 78 ° + i \sin 78 °)

B

z_{1} z_{2} = 8 (\cos 78 ° + i \sin 78 °)

C

z_{1} z_{2} = 15 (\cos 78 ° - i \sin 78 °)

D

z_{1} z_{2} = 8 (\cos 78 ° - i \sin 78 °)

Question 5: Find

z_{1} z_{2}

, where

z_{1} = 4 (\cos 31 ° + i \sin 31 °)

and

z_{2} = 7 (\cos (- 12 °) + i \sin (- 12 °))

A

z_{1} z_{2} = 11 (\cos 19 ° - i \sin 19 °)

B

z_{1} z_{2} = 28 (\cos 19 ° + i \sin 19 °)

C

z_{1} z_{2} = 28 (\cos 43 ° - i \sin 43 °)

D

z_{1} z_{2} = 28 (i \sin 43 ° - \cos 43 °)

Test: Complex Numbers III - Ambitious