Question

Write -2+2i in polar form (ans in degrees)

Answer 1

Answer:

2sqrt(2)cis(135)

2sqrt(2)e^(135i)

2sqrt(2)[cos(135)+isin(135)]

Step-by-step explanation:

The number is in form x+yi.

If x=y or x=-y, then we know we will need an angle measurement that is a multiple of 45 degrees; more accurately of the form (2k+1)45 degeees where k is an integer.

Since x is negative and y is positive, we are in the second quadrant. That means theta is 45(3) or 135 degrees.

At 135 degrees, we have the point

(-sqrt(2)/2,sqrt(2)/2). (Notice that x=-y).

-2+2i

Factor out 2:

2(-1+1i)

Multiply by 1 so that we can use the point mention. Namely, 2/sqrt(2) × sqrt(2)/2:

2 ×2/sqrt(2) (-sqrt(2)/2+sqrt(2)/2 i)

Simplify:

4/sqrt(2) (-sqrt(2)/2+sqrt(2)/2 i)

Continue to simplify:

4sqrt(2)/2 (-sqrt(2)/2+sqrt(2)/2 i)

Simplifying:

2sqrt(2)(-sqrt(2)/2+sqrt(2)/2 i)

Polar form is therefore

2sqrt(2)cis(135)

Or

2sqrt(2)e^(135i)

I don't know your exact desired polar form.

Could also be

2sqrt(2)[cos(135)+isin(135)].