Question

$z_1$ (3, 2), $z_2$ (1, 5) and origin O form a triangle. Find the angle between the sides O$z_1$ and O$z_2$

• A. 30
• B. 60
• C. 45
• D. 90

Answer 1

The correct option is C

45

$\frac{z_2}{z_1}$ = $\left|\frac{z_2}{z_1}\right|$ $e^{i\theta }$

$\theta$ = arg $\left(\frac{z_2}{z_1}\right)$

= Arg $\left(\frac{1+5i}{3+2i}\right)$

= Arg $\left(\frac{(1+5i)(3-2i)}{(3+2i)(3-2i)}\right)$

= Arg $\left(\frac{(3+10)+i(-2+15)}{13}\right)$

= Arg(1+i)

=45