Question

The value of The value of $\frac{2(\cos \, 75^{\circ} + i \, \sin \, 75^{\circ})}{0.2(\cos \, 30^{\circ} + i \, \sin \, 30^{\circ})}$ is

• A. $\frac{5}{\sqrt{2}} (1 + i)$
• B. $\frac{10}{\sqrt{2}} (1 + i)$
• C. $\frac{10}{\sqrt{2}} ( 1 - i ) $
• D. $\frac{5}{\sqrt{2}} (1 - i)$

Answer 1

The Correct Option is B

$\frac{2\left(\cos 75^{\circ}+i \sin 75^{\circ}\right)}{0.2\left(\cos 30^{\circ} i \sin 30^{\circ}\right)}= \frac{2 \cdot e^{i 75^{\circ}}}{0.2 \cdot e^{i 30^{\circ}}}$
$\left(\because \cos \theta +i \sin \theta=e^{i \theta}\right)$
$=10 \cdot e^{i 75^{\circ}} \cdot e^{-i 30^{\circ}}$
$=10 \cdot e^{i 45^{\circ}}$
$=10\left(\cos 45^{\circ}+i \sin 45^{\circ}\right)$
$\left(e^{i \theta}=\cos \theta +i \sin \theta\right)$
$= 10\left(\frac{1}{\sqrt{2}}+i \frac{1}{\sqrt{2}}\right)$
$=\frac{10}{\sqrt{2}}(1+i)$