Question

The line joining the origin and the point represented by the complex number z = 1 + i is rotated through an angle 3π/2 in anticlockwise direction about the origin and stretched by additional $\sqrt{2}$ unit. In the new position, the point is represented by the complex number

• A. – $\sqrt{2}$– $\sqrt{2}$I
• B. $\sqrt{2}$ – $\sqrt{2}$i
• C. 2 – $\sqrt{2}$I
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Sol. If z₁ be the new complex number then

|z₁| = |z| +$\sqrt{2}$= 2 $\sqrt{2}$.

Also $\frac{z_{1}}{z} = \frac{\left| z_{1} \right|}{|z|}e^{i3\pi/2}$ ⇒ z₁ = z. 2$\left( \cos\frac{3\pi}{2} + i\sin\frac{3\pi}{2} \right)$

= 2(1+ i) (0 – i) = – 2i +2 = 2(1 – i)