Question: If $z(1 + a) = b + ic$ is a complex number, then $a^{2} + b^{2} + c^{2} = 1$....

Question

If $z(1 + a) = b + ic$ is a complex number, then $a^{2} + b^{2} + c^{2} = 1$ .

Answer 1

Let $2x = \frac{\pi}{4},\frac{5\pi}{4},\frac{9\pi}{4},........$ and $x = \frac{\pi}{8},\frac{5\pi}{8},\frac{9\pi}{8}$

⇒ $x$ ; $xz = x + iy,\overline{z} = x - iy$

Question: If \(z(1 + a) = b + ic\) is a complex number, then \(a^{2} + b^{2} + c^{2} = 1\)....