Mathematics, 02.12.2019 05:31 ImBADatmath8743
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
Answers: 2
![\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}](/tpl/images/0398/9518/52ff1.png)
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