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How do I find the product z1z2 if z1 5(cos20 plus isin20) and z2 8(cos15 plus isin15)?
Updated: 10/18/2022
Wiki User
∙ 6y agoBest Answer
Like normal expansion of brackets, along with:
cos(A + B) = cos A cos B - sin A sin B
sin(A + B) = sin A cos B + cos A sin B
5(cos 20 + i sin 20) × 8(cos 15 + i sin 15)
= 5×8 × (cos 20 + i sin 20)(cos 15 + i sin 15)
= 40(cos 20 cos 15 + i sin 15 cos 20 + i cos 15 sin 20 + i² sin 20 sin 15)
= 40(cos 20 cos 15 - sin 20 cos 15 + i(sin 15 cos 20 + cos 15 sin 20))
= 40(cos(20 +15) + i sin(15 + 20))
= 40(cos 35 + i sin 35)
Wiki User
∙ 6y agoThis answer is:
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