Question

Soal tentang bilangan kompleks , mohon bantuannya kak

Answer 1

A. z1 × z2
= 2(cos 30° + i sin 30°) × 3(cos 60° + i sin 60°)
= 2(1/2√3 + i . 1/2) × 3(1/2 + i . 1/2√3)
= (√3 + i) × (3/2 + 3/2√3i)
= 3/2√3 - 3/2√3 + 9/2i + 3/2i
= 12/2i
= 6i

b. z1 : z2
= 2(cos 30° + i sin 30°) / 3(cos 60° + i sin 60°)
= 2(1/2√3 + i . 1/2) / 3(1/2 + i . 1/2√3)
= (√3 + i) / (3/2 + 3/2√3i)
= [ (√3 + i)(3/2 + 3/2√3i) ] / [ (3/2 + 3/2√3i)(3/2 - 3/2√3i) ]
= (3/2√3 - 3/2√3 + 9/2i + 3/2i) / [ (3/2)² + (3/2√3)² ]
= (6i) / (9/4 + 27/4)
= (6i) / (36/4)
= (6i) / 9
= (2i) / 3