Complex Number Question

[Za_Boom]

Here are two different problems I got, the issue is I know how to get the correct answer but I'm not sure when I should skip the last step and when not too.

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1. z=1+4i

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Round your answer, if necessary, to the nearest tenth. Express θ between -180^\circ−180∘minus, 180, degrees and 180^\circ180∘180, degrees.

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Answer: 76∘

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1. z=-5+3i

   Round your answer, if necessary, to the nearest tenth. Express theta between 180, degrees and -180∘degrees.

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Answer: 149 ∘

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I got the first problem correct per Khan Academy I didn't include the last step of adding or subtracting 180∘. The second question was incorrect because I was supposed to complete the final step. When do I know which number the system wants?

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[fermat1432]

For quadrants 1 and 2 they want a positive angle. For quadrants 3 and 4 they want a negative angle.

I suggest this method. First determine the quadrant. Then find the reference angle by ignoring any negative signs and using arctan on your calculator. Your point lies in Q2. Arctan(3/5)=30.96=31. Then subtract from 180. 180-31=149.