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Write the trigonometric form of the complex number. (Round your angles to two decimal places. Let 0 ≤ < 2.)

Write the trigonometric form of the complex number. (Round your angles to two decimal-example-1
User Klick
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Given a complex number z:


z=a+bi

We can write this number in trigonometric form, using:


\begin{gathered} z=r(\cos\theta+i\sin\theta) \\ . \\ a=r\cos\theta \\ . \\ b=r\sin\theta \\ . \\ r=√(a^2+b^2) \end{gathered}

In this case, we are given:


z=-8+2i

We need to find r and θ. We know:

· a = -8

· b = 2

Thus:


r=√((-8)^2+2^2)=√(64+4)=√(68)=2√(17)

And now, we can find θ:


-8=2√(17)\cos\theta

And solve:


\begin{gathered} \cos\theta=-(8)/(2√(17)) \\ . \\ \theta=\cos^(-1)(-(4√(17))/(17))\approx2.89661 \end{gathered}

Now we can write the number in trigonometric form:


z=2√(17)(\cos(2.9)+i\sin(2.9))

User Eugene Karataev
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