How do you multiply (7(cos 23+isin 23)) (4(cos 7+isin 7))?

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How do you multiply (7(cos 23+isin 23)) (4(cos 7+isin 7))?

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Answer 1 · 2018-05-17T00:32:37

Given: $(7 (cos (23) + i sin (23))) (4 (cos (7) + i sin (7)))$ $(7(cos(23)+isin(23))) (4(cos(7)+isin(7)))$

7 is the magnitude of the first factor and 4 is the magnitude of the second factor.

I multiply the magnitudes:

$7 (4) = 28$ $7(4) = 28$

$23$ $23$ is the angle of the first factor and $7$ $7$ is the angle of the second factor.

I add the angles:

$23 + 7 = 30$ $23+7 = 30$

This the process for multiplication in the trigonometric form:

$(7 (cos (23) + i sin (23))) (4 (cos (7) + i sin (7))) = 28 (cos (30) + i sin (30))$ $(7(cos(23)+isin(23))) (4(cos(7)+isin(7)))= 28(cos(30)+isin(30))$

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How do you multiply (7(cos 23+isin 23)) (4(cos 7+isin 7))?

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