find z. [z+2-j]/[z+1]= -1.554-0.644i how to find z?

Question

z answer is -0.197+0.09i

Answer 1

I'm guessing that z is complex, so write it as a+jb, plug that in for z, do the arithmetic, and you'll get something that looks like
a+jb = n+mj where n and m are numerical values and that's your complex value for z.

Doug

Answer 2

Let z = a+ib and [z+2-i]/[z+1] = M+Ni

M+Ni = [(a+2)+(b-1)i] / [(a+1)+ib]

Multiply conjugate, [(a+1)-ib]/[(a+1)-ib] and comparing real and imaginary element respectively.

Real coefficient: M
M = [(a+2)(a+1) + b(b-1)] / [(a+1)^2+b^2]

Imaginary coefficient: N
N = [(b-1)(a+1) - b(a+2)] / [(a+1)^2+b^2]

Finally
z.[z+2-i]/[z+1]
= (a+ib)(M+Ni)
= (aM-bN) + i(bM+aN)