If-z-2-1-z-2-1-then-z-lies-on-

Question Number 19740 by Tinkutara last updated on 15/Aug/17

If ∣ z^{2} - 1 ∣ = ∣ z ∣^{2} + 1, then z lies on

Answered by ajfour last updated on 16/Aug/17

∣ {(x + iy)}^{2} - 1 ∣= x^{2} + y^{2} + 1

\Rightarrow {(x^{2} - 1 - y^{2})}^{2} + {4 x}^{2} y^{2} = {(x^{2} + 1 + y^{2})}^{2}

\Rightarrow {4 x}^{2} y^{2} = {2 x}^{2} ({2 y}^{2} + 2)

x^{2} (y^{2} + 1 - y^{2}) = 0

\Rightarrow x = 0

z lies on the imaginary axis .

Commented by Tinkutara last updated on 15/Aug/17

Thank you very much Sir!