Question Number 230 by ssahoo last updated on 25/Jan/15
![Let z and w be two complex numbers such that ∣z∣≤1 , ∣w∣≤1 and ∣z+iw∣=∣z−iw^(−) ∣=2, then find the value of z.](https://www.tinkutara.com/question/Q230.png)
$$\mathrm{Let}\:{z}\:\mathrm{and}\:{w}\:\mathrm{be}\:\mathrm{two}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mid{z}\mid\leqslant\mathrm{1}\:,\:\mid{w}\mid\leqslant\mathrm{1}\:\mathrm{and}\:\mid{z}+{iw}\mid=\mid{z}−{i}\overline {{w}}\mid=\mathrm{2}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{z}. \\ $$
Commented by 123456 last updated on 16/Dec/14
![∣z+iw∣≤∣z∣+∣w∣≤2 ∣z−iw^](https://www.tinkutara.com/question/Q233.png)