Given w is equal to square root of 2 times open paren cosine of open paren pi over 4 close paren plus i sine open paren pi over 4 close paren close paren and z is equal to 2 times open paren cosine of open paren pi over 2 close paren plus i sine open paren pi over 2 close paren close paren , what is w minus z expressed in polar form?

Using the values at the special angles, w = √2(cos π/4 + i sin π/4) = 1 + i, and z = 2(cos π/2 + i sin π/2) = 2i. Thus w − z = 1 − i. Its modulus is √(1² + (−1)²) = √2, and its angle is 7π/4 because the point (1, −1) lies in the fourth quadrant. Therefore the polar form is √2(cos 7π/4 + i sin 7π/4), choice A.

AI-written and checked against the verified answer.