Question

The complex numbers w

and z satisfy the relation w= (z + i)/ (iz + 2)

Given that z = 1 + i, find w. giving your answer in the form x + iy, where x and y are real.​

Answer 1

`w=(1+i+i)/(i(1+i)+2)\\\\w=(1+2i)/(i-1+2)\\\\w=(1+2i)/(1+i)\\\\w=((1+2i)(1-i))/(1+1)\\\\w=(1-i+2i+2)/(2)\\\\w=(3+i)/(2)\\\\w=(3)/(2)+(1)/(2)i`