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 ((11\pi)/(6))+j\sin ((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 ((\pi)/(6))=\frac{\sqrt[]{3}}{2} \\ \\ \sin ((\pi)/(6))=(1)/(2) \end{gathered}`

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

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

So, the answer will be option B.