Question

In the following figure , if AB = 2BC and $\alpha =\frac{\pi }{2}$, then find the co-ordinates of A($Z_2$)

• A. (1+3i)
• B. (1-3i)
• C. (-1+3i)
• D. (-1-3i)

Answer 1

The correct option is A

(1+3i)

$\frac{z_2-z}{z_1-z}$ = $\left|\frac{z_2-z}{z_1-z}\right|$ $\times$ $e^{i\alpha }$

= 2 × $e^{i\frac{\pi }{2}}$

$\frac{z_2-(1+i)}{(2+i)-(1+i)}$ = 2i

$\Rightarrow$ $z_2$ = (1+i) + 2i $\times$ 1

= 1 + 3i