How do I find the product z1z2 if z1 5(cos20 plus isin20) and z2 8(cos15 plus isin15)?

Answer 1

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)