Question

Perform the operation shown below and leave the result in trigonometric form.

[8(cos10° + i sin10°)] [5(cos 200° + i sin 200°)]

Answer 1

Lottie and Jessica -- please don't switch names. It's pointless.

Answer 2

[8(cos10° + i sin10°)] [5(cos 200° + i sin 200°)]
= 40(cos10° + i sin10°)(cos 200° + i sin 200°)
= 40 ( cos10cos200 + i(cos10sin200) + i(sin10cos200) + i^2 sin10sin200)

= 40( cos10cos200-sin10sin200 + i(sin10cos200 + cos10sin200) , recall i^2 = -1

= 40( cos(10+200) + i sin(10 + 200) )
= 40 (cos 210 + i sin 210)
= 40(-√3/2 - (1/2) i )
= -20√3 - 20 i

check my arithmetic

Answer 3

or, more directly, using deMoivre:

8cis10 * 5cis200
= 8*5 cis(10+200)
...