Write z = 2(sqrt)2 + 2(sqrt)2i in polar form.

Question

z = 4(sqrt)2 (cos pi/4 + i sin pi/4)
z = 4 (cos pi/4 + i sin pi/4)
z = 4 (cos 5pi/4 + i sin 5pi/4)
z = 4 (cos pi/2 + i sin pi/2)

Write z = -6i in polar form.

z = 6 cis 3pi/2
z = 6 cis pi/2
z = -6 cis 3pi/2
x = 6(sqrt)2 cis 3pi/2

I've tried figuring these two out but I need help

Answer 1

z = 2√2 + 2√2 i
r = √(8+8) = 4
tanØ = 2√2/(2√2) = 1
Ø = π/4

z = 4(cosπ/4 + i sinπ/4) or 4cisπ/4 , if you learned that abbreviation

for z = -6i
consider it as z = 0 - 6i and proceed as before
from the graph in the Argand plane , it can be seen that the angle is 3π/2

which of the answer choices would apply ?

Answer 2

The third one: z = -6 cis 3pi/2

Answer 3

Whoops I'm wrong it's the first one

Answer 4

Yup, it is +6
the r value is considered positive, the direction will be take care
of by the angle.

Answer 5

The full answers for the practice are:
B. z = 4(cos pi/4 + i sin pi/4)
A. z = 6 cis 3pi/2
D. z = 4sqrt3 - 4i
B. z = -2.25 - 1.1i

Answer 6

Thank you for providing the correct answers!