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bija089 [108]
2 years ago
6

I) Express Z1 in polar Form a) Z1=1-(2-√3)i (complex number)

Mathematics
2 answers:
Marianna [84]2 years ago
8 0

Answer:

z_1=1-(2-\sqrt{3})i=2\sqrt{2-\sqrt{3}}[cos(\frac{23\pi}{12} )+isin(\frac{23\pi}{12} )]

Step-by-step explanation:

Recall that a+bi=r(cos\theta+isin\theta) where r=\sqrt{a^2+b^2} and \theta=tan^{-1}(\frac{b}{a}).

Since a=1 and b=-2+\sqrt{3}, then r=\sqrt{(1)^2+(-2+\sqrt{3})^2}=2\sqrt{2-\sqrt{3}} and \theta=tan^{-1}(\frac{-2+\sqrt{3}}{1})=-\frac{\pi}{12}=\frac{23\pi}{12}.

Therefore, z_1=1-(2-\sqrt{3})i=2\sqrt{2-\sqrt{3}}[cos(\frac{23\pi}{12} )+isin(\frac{23\pi}{12} )]

kicyunya [14]2 years ago
7 0

Step-by-step explanation:

hope it will help you thank you

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What is the solution to -5x-7≤2?
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