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Write the trigonometric form of the complex number. (Let 0 ≤ < 2.)1 − √3iradical 3i

User Jaquan
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2 Answers

12 votes
12 votes
the answer to your question is i am pretty sure 26
User Yurmix
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30 votes
30 votes

Solution

We have the following number:


1-\sqrt[]{3}i

and we have:


a=1,b=-\sqrt[]{3}

And we can write the trigonometric form as:


r(\cos \theta+i\sin \theta)

the radius is:


r=\sqrt[]{(1)^2+(-\sqrt[]{3})^2}=\sqrt[]{4}=2

The angle is:


\theta=\tan ^(-1)(\frac{-\sqrt[]{3}}{1})=(5\pi)/(3)

Then the answer is:


2\lbrack\cos ((5\pi)/(3))+i\sin ((5\pi)/(3))\rbrack

User Wale
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