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Rosario J.

Precalculus

4 days, 7 hours ago

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given z1 = -3(cos(32°)+i sin(32°)) and z2 = -10(cos(13°)+i sin(13°)). find the product of z1z2. what is the exact? answer

you want to find the product of these two complex numbers. So what you're gonna do is you're gonna use um the formula that goes like this. If forget the letters that you use let's let's just say cosigning A. A. Cause I'm B plus ice time be and then it was easy to was C. Co sign D. Plus I. Sine D. Then Z1Z 2 would be a time. See Kassian B plus D. Plus I sine be plus de. Okay so you multiply the numbers in the front, the lengths sort of and then you add the angles together. Okay so in your case you're going to have Z. one Z. two equals negative three times negative 10 Times the cosine of 32 plus 13 plus I sine 32 Plus 13. So that's 30 times the cosine of 45 Plus I signed 45. Okay so 45° that triangles 11 squared of two. So this is 30 times one over the square to to plus I times one over the square root of two. Okay so maybe it would be easier if instead of I instead of putting in one over the square root of two, I put in the square root of 2/2. Okay. Same thing. Alright so then when you multiply through you get 15 times the square to to plus I. 15 square roots. So to so that's the product of those two numbers

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