Question

Let z=-8+15i and w=6-8i. Compute

zz/ww


(each of the second ones, z and w, have a bar over them)

where the bar represents the complex conjugate.

Answer 1

recall that if

z = x+iy
zz* = (x+iy)(x-iy) = x^2+y^2

Answer 2

z = -8+15i and w = 6-8i. The equation would be ((-8 + 15i)(-8 - 15i))/((6 - 8i)(6+8i) Then you expand the binomials. That equals 64 + 120i - 120i - 225i^2. Then the two 120i's cancel to get 64 - 225i^2 for the numerator. Then you simplify the denominator the same way to get 36 + 24i - 24i - 64i^2. Again the 24i's cancel to get 36 - 64i^2. i^2 = -1, so (64 - 225(-1)) / (36 - 64(-1)) = (64 + 225) / (36 + 64). then you get the fraction 289/100.

289/100 is the answer