Question

Convert the polar representation of this complex number into its standard form. 2 COS (600 (179 11T + sin 6 () 117 6 O A. 1 - 131 O B. 3 - 1 O C. - 3 + 1 O D. & 13 1 2 2 1 / 1

Answer 1

Given:

$2(\cos (\frac{11\pi}{6})+j\sin (\frac{11\pi}{6}))$

The given complex number need to convert it a polar form

The angle (11π/6) lying on the fourth quadrant

So, cos (11π/6) will be (+) and sin (11π/6) will be (-)

The reference angle will be: 360 - (11π/6) = π/6

$\begin{gathered} \cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2} \\ \\ \sin (\frac{\pi}{6})=\frac{1}{2} \end{gathered}$

So, the standard form of the given number will be:

$\begin{gathered} 2\cdot(\frac{\sqrt[]{3}}{2}-j\frac{1}{2}) \\ \\ =\sqrt[]{3}-j \end{gathered}$

So, the answer will be option B.