Question

Convert the polar representation of this complex number into its standard form.

Answer 1

$2(cos(\frac{7 \pi}{6})+i\ sin(\frac{7 \pi}{6}))\\\\2((-\frac{\sqrt{3}}{2})+i(-\frac{1}{2}))\\\\\\-\sqrt{3}-i$

Answer 2

Answer:

Option A is correct

The standard form is

$2(\cos{\frac{7\pi}{6}}+i\sin{\frac{7\pi}{6}})=-\sqrt3-i$

Step-by-step explanation:

Given the polar representation of complex number

$2(\cos{\frac{7\pi}{6}}+i\sin{\frac{7\pi}{6}})$

we have to convert the above polar representation in standard form.

The standard form of a complex number is a+ib

where a is the real part and bi is the imaginary part.

$2(\cos{\frac{7\pi}{6}}+i\sin{\frac{7\pi}{6}})$

$=2\cos{\frac{7\pi}{6}}+2i\sin{\frac{7\pi}{6}}$

$=2\times (\frac{-\sqrt3}{2})+2i\times (\frac{-1}{2}}$

$=-\sqrt3-i$

which is required standard form.

Hence, option A is correct.