Question

Find the product of the complex numbers

z, = 5( cos 20° + i sin 20°)

za = 4( cos 10° + i sin 10°)

Answer 1

17.32 + 10i

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