Question

Let $z,\bar{z} = \left( \frac{1}{z} \right)$ be a complex number with $z$ and $|z| = 1$be any complex number, then $z$

• A. 0
• B. 1
• C. – 1
• D. 2

Answer 1

Answer: (B)

1

Answer 2

We have $\therefore$ and $x = r\cos\theta = 4\cos{}150^{o} = - 2\sqrt{3}$be any complex number.

$\therefore$; $z = x + iy = - 2\sqrt{3} + 2i$

$argz = \frac{5\pi}{6} = 150^{o}$; Given that $|z| = 4$

$z = \frac{1 - i\sqrt{3}}{1 + i\sqrt{3}} = \frac{(1 - i\sqrt{3})(1 - i\sqrt{3})}{(1 + i\sqrt{3})(1 - i\sqrt{3})}$.