The trigonometric form of a complex number
Answers are for parents and teachers.
1
Write z = ββ3 + i in trigonometric form.
2(cos 5Ο/6 + i sin 5Ο/6)
2
Find the modulus and argument of z = 1 β i.
Modulus β2, argument 7Ο/4.
3
Compute 2(cos 70Β° + i sin 70Β°) Β· 3(cos 50Β° + i sin 50Β°) and write it in algebraic form.
6(cos 120Β° + i sin 120Β°) = β3 + 3β3 i
4
Compute (β3 + i)βΆ.
β64
5
Why does multiplying in trigonometric form add the arguments? Which formula does it rely on?
The formulas cos Οβ cos Οβ β sin Οβ sin Οβ = cos(Οβ + Οβ) and sin Οβ cos Οβ + cos Οβ sin Οβ = sin(Οβ + Οβ): they are exactly what appears when multiplying.