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Convert the polar representation of this complex number into its standard form.
2(cos(7pi/6)+isin(7pi/6))

A.) -sqrt(3)-i
B.) 1-sqrt(3) i
C.) -sqrt(3)/2-1/2i
D.) sqrt(3)-1
*Need help please*

Respuesta :

Apocrophon
[tex]2(cos(\frac{7 \pi}{6})+i\ sin(\frac{7 \pi}{6}))\\\\2((-\frac{\sqrt{3}}{2})+i(-\frac{1}{2}))\\\\\\-\sqrt{3}-i[/tex]

Answer:

Option A is correct

The standard form is

[tex]2(\cos{\frac{7\pi}{6}}+i\sin{\frac{7\pi}{6}})=-\sqrt3-i[/tex]

Step-by-step explanation:

Given the polar representation of complex number

[tex]2(\cos{\frac{7\pi}{6}}+i\sin{\frac{7\pi}{6}})[/tex]

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.

[tex]2(\cos{\frac{7\pi}{6}}+i\sin{\frac{7\pi}{6}})[/tex]

[tex]=2\cos{\frac{7\pi}{6}}+2i\sin{\frac{7\pi}{6}}[/tex]

[tex]=2\times (\frac{-\sqrt3}{2})+2i\times (\frac{-1}{2}}[/tex]

[tex]=-\sqrt3-i[/tex]

which is required standard form.

Hence, option A is correct.

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