Question

In Argand diagram, O, P, Q represents the origin, $z$ and $z+iz$
respectively. then $\angle OPQ=$

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is C $\frac{\pi }{2}$

$z=x+iy$

$z+iz=(x+iy)+i(x+iy)$

$=x+iy+xi-y$

$=(x-y)+(x+y)i$

Slope of line $PQ=\frac{x+y-y}{x-y-x}=\frac{-x}{y}=m_1$

Slope of $OP=\frac{y}{x}=m_2$

$m_1{m}_2=-1$

lines are perpendicular. $\angle OPQ={90}^{\circ }=\frac{\pi }{2}$

C is correct.