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Hello everybody and welcome.
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We want to represent the complex number graphically and find its trigonometric form.
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So we have 1 minus root 3i.
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So first we have to find it uh represent it trigonmetrically.
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So we know this is going to be in the form of r cosine theta plus i sine theta.
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So we have to find r and theta.
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So to find r we know r squared is equal to x squared plus y squared.
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So r is equal to the square root of x squared.
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So x is just the real part of the complex number and y is just the imaginary part.
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So r is equal to the squared of 1 plus 3, r is equal to the square of 4, which is equal to 2.
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Next, you have to find the theta, so tan theta is equal to y over x.
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Tan theta is equal to negative root 3 over 1, and therefore theta is equal to 5 pi over 3.
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So next, we are just going to put this, plug these back into our equation right over here, and we get our final answer, which is 2 times the cosine of 5 pi over 3, plus i times the sign of 5 pi over 3.
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And so this is going to be our answer in trigonometric form...