Convert the following from standard form to trigonometric form: -1-i?

Question

I have done this and arrived at sqrt2 cis45 but it is wrong and I don't know why or how to get the right anser. Can anyone help. please? Thanks!

Answer 1

Write it as -1*(1+i). Now 1+ i = sqrt(2)/_pi/4 = sqrt(2) cis 45
and multiplying it by -1 rotates it counterclockwise by pi.
Why? Because -1 = 1/_ pi = 1 cis 180.
So the answer is sqrt(2)/_5*pi/4 or sqrt(2) cis 225.
Hope that helps!

Answer 2

z = a + b i
From trig. identities:
a = r cos q
b = r sin q
z = r ( cos q + i sin q )

r = sqrt(a^2 +b^2)
r = sqrt(1 + 1)
r = sqrt(2)

That means
-1 = sqrt(2) cos q and
-1 = sqrt(2) sin q
or
-1/sqrt(2) = cos q and -1/sqrt(2) = sin q
This implies that 45 degrees is the reference angle.
Since cos and sin are both negative that means it is in the third quadrant.
The angle you are looking for is 180+45 = 225 degrees