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. $\frac{5}{\sqrt{2}}(1-i)$
• E. $\frac{1}{\sqrt{2}}(1+i)$

Answer 1

Answer: (B)

$\frac{2\left(\cos 75^{\circ }+i\sin 75^{\circ }\right)}{0.2\left(\cos 30^{\circ }i\sin 30^{\circ }\right)}=\frac{2\cdot e^{i75^{\circ }}}{0.2\cdot e^{i30^{\circ }}}$
$\left(\because \cos \theta +i\sin \theta =e^{i\theta }\right)$
$=10\cdot e^{i75^{\circ }}\cdot e^{-i30^{\circ }}$
$=10\cdot e^{i45^{\circ }}$
$=10\left(\cos 45^{\circ }+i\sin 45^{\circ }\right)$
$\left(e^{i\theta }=\cos \theta +i\sin \theta \right)$
$=10\left(\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}\right)$
$=\frac{10}{\sqrt{2}}(1+i)$