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

Sagot :

Solution

We have the following number:

[tex]1-\sqrt[]{3}i[/tex]

and we have:

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

And we can write the trigonometric form as:

[tex]r(\cos \theta+i\sin \theta)[/tex]

the radius is:

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

The angle is:

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

Then the answer is:

[tex]2\lbrack\cos (\frac{5\pi}{3})+i\sin (\frac{5\pi}{3})\rbrack[/tex]

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