Question

Find the complex number $\mathcal{Z}$, if $|\mathcal{Z}+1|=\mathcal{Z}+2\left(1+i\right)$.​

Answer 1

squaring on both the sides

z²+1+2z = z² + 4z (1+i) + 4+i²

but i² = -1

1+2z = 4z +4z√-1 -4

5 = 2z + 4√-1

z = 5 - 4√-1