Question

find the (conjugate of z) times (w)
if z=[3,120]
and w=[-1,-15]

Answer 1

If z = [3,120] is your way of writing
z = 3 + 120i, then the conjugate of z is z' = 3 - 120i
The product of z' and w = -1 - 15i is
-3 -1800 -45i +120i = -1803 +75i

If I am not interpreting your notation correctly, then please explain what [a,b] means.

When the same problem was posted last night, I assumed you were asking for the (conjugate of) the z times w. The answer was therefore different

Answer 2

[a,b] is [r,theta] or polar form

Answer 3

Thank you for explaining your notation. With your notation now explained, the conjugate of z is [3,-120]. If you are using [r, theta] notation, when talking about w, how can r be -1? I have to assume that r=-1 at theta = -15 is the same as r = +1 pointed in the opposite direction, theta = 165.

For the product of z' and w, r-values get multipled and the polar angles get added, so the r value is 3 and theta is 165 -120 = 45 degrees, resulting in [3,45]