The complex number cosθ + i sinθ


The complex number cosθ + i sinθ __________ be zero for any θ.


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.

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