The complex number cosθ + i sinθ
Question:
The complex number cosθ + i sinθ __________ be zero for any θ.
Solution:
z = cosθ + i sinθ can never be zero for any θ because z = 0
⇒ cosθ = 0 and sin θ = 0
Since no such value of θ exists
⇒ cosθ + i sinθ can never be zero.