Question

If |$\sqrt{2}$z – 3 + 2i | = | z | $\left| \sin\left( \frac{\pi}{4} + \arg z_{1} \right) + \cos\left( \frac{3\pi}{4} - \arg z_{1} \right) \right|$,

Where z₁ = 1 + $\frac{1}{\sqrt{3}}$i, then locus of z is

• A. Pair of straight lines
• B. Circle
• C. Parabola
• D. Ellipse

Answer 1

Answer: (B)

Circle

Answer 2

Sol. arg (z₁) = $\frac{\pi}{6}$

Ž sin $\left( \frac{\pi}{4} + \arg z_{1} \right)$+ cos$\left( \frac{3\pi}{4} - \arg z_{1} \right) = \frac{1}{\sqrt{2}}$

\ | $\sqrt{2}$ z – 3 + 2i | = | z | $\frac{1}{\sqrt{2}}$

Ž $\begin{matrix} \frac{z - \frac{3 - 2i}{\sqrt{2}}}{z} \end{matrix} = \frac{1}{2}$

which represents a circle