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yawa3891 [41]
3 years ago
10

PRECALC QUESTION! Convert the polar representation of this complex number into its standard form: z = 2(cos 11pi/6+ i sin 11pi/6

)? A. sqrt(3) -i B. 1- sqrt(3) i C. -sqrt(3)/ 2 -(1/2) i D. -sqrt(3) + i
Mathematics
2 answers:
Tanzania [10]3 years ago
7 0
\bf z=2\left[ cos\left( \frac{11\pi }{6} \right) + i\ sin\left( \frac{11\pi }{6} \right) \right]\qquad 
\begin{cases}
r=2\\
\theta=\frac{11\pi }{6}\\
-----\\
a=x=rcos(\theta)\\
b=y=rsin(\theta)
\end{cases}\implies a+bi
\\\\\\
2cos\left( \frac{11\pi }{6} \right)+2sin\left( \frac{11\pi }{6} \right)\ i\implies 2\cdot \cfrac{\sqrt{3}}{2}+2\cdot \cfrac{-1}{2}\ i\implies \sqrt{3}-1i
\\\\\\
\boxed{\sqrt{3}-i}
Harrizon [31]3 years ago
5 0

Answer:

Option A - z=\sqrt{3}-i

Step-by-step explanation:

Given : Polar representation of complex number  z=2[\cos( \frac{11\pi }{6}) + i\sin( \frac{11\pi }{6} )]

To find : Convert the polar representation of this complex number into its standard form?

Solution :

z=2[\cos(\frac{11\pi }{6}) + i\sin(\frac{11\pi }{6})]

The given complex number is in the form, z=r(\cos\theta+i\sin\theta)

Where, r=2 and \theta=\frac{11\pi }{6}

The standard form of complex number is z=x+iy

Where, a=x=r\cos\theta\\b=y=r\sin\theta

2\cos( \frac{11\pi }{6})+2\sin( \frac{11\pi }{6})\ i\implies 2\cdot \cfrac{\sqrt{3}}{2}+2\cdot \cfrac{-1}{2}\ i\implies \sqrt{3}-1i\\\\\boxed{z=\sqrt{3}-i}  

Therefore, Option A is correct.

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