5) find the complex number z and w such that z+w=4+3i and z-iw=3-2i

Answer 1

subtract them:
w + iw = 4+3i -3 + 2i
w(1+i) = 1 + 5i
w = (1+5i)/(1+i)
"realizing" the denominator
w = (1+5i)/(1+i) * (1-i)/(1-i)
= (1 + 5i - i - 5i^2)/(1 - i^2)
= (6 + 4i)/2 = 3 + 2i

then in z+w = 4+3i
z + 3+2i = 4+3i
z = 1+i

Answer 2

thanks! very clear now