SOLUTION: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. −3 + 6i

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Question 1170518: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
−3 + 6i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
-3%2B6i=r%28cos%28theta%29%2Bi%2Asin%28theta%29%29

r=sqrt%28a%5E2%2Bb%5E2%29.............a=-3,b=6
r=sqrt%28%28-3%29%5E2%2B6%5E2%29
r=sqrt%289%2B36%29
r=sqrt%2845%29
r=3sqrt%285%29
r=6.71
theta=tan%5E-1%28b%2Fa%29%2B180°
theta=tan%5E-1%286%2F-3%29%2B180°
theta=-63.43%C2%B0%2B180°
theta=116.57°
then we have:
-5%2B12i=6.71%28cos%28116.57%29%2Bi%2Asin%28116.57%29%29

or
r=6.71,theta=116.57°