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)].
