Find the product of the complex numbers

z, = 5 (cos 20° + i sin 20°)

za = 4 (cos 10° + i sin 10°)

17.32 + 10i

Step-by-step explanation:

The product of the complex numbers;

z, = 5 (cos 20° + i sin 20°)

za = 4 (cos 10° + i sin 10°)

5 (cos 20° + i sin 20°) * 4 (cos 10° + i sin 10°)

= 20 (cos20 (cos10) + i sin20 (cos10) + i sin10 (cos20) + isin20 (i sin10))

= 20 (cos20 (cos10) + i sin20 (cos10) + i sin10 (cos20) + sin20 (sin10) i^2)

And i^2 = - 1

= 20 (cos20 (cos10) + i sin20 (cos10) + i sin10 (cos20) - sin20 (sin10))

= 20 (cos20 (cos10) - sin20 (sin10) + i (sin20 (cos10) + sin10 (cos20)))

= 20 (0.866 + i (0.5))

= 17.32 + 10i