Question

i) write the conjugate of the complex number. cos θ + i sin θ​

Answer 1

Answer:

cosθ-i sinθ

Step-by-step explanation:

The conjugate of the complex number is cosθ-i sinθ.

Answer 2

Conjugate of the complex number  cos θ + i sin θ​  is cos(-θ) + i sin (-θ​)

Conjugate of complex number a + ib is  a - ib

polar form is r(cos θ + i sin θ)

cos θ + i sin θ  value of  r= 1

Comparing cos θ + i sin θ​  with a + ib

a = rcos θ = cos θ

b = rsin θ =  sin θ

Conjugate of a + ib is  a - ib

= a + i(-b)

Using  cos x = cos(-x)  and  sin(-x) = - sinx

a = cos θ = cos(-θ)

-b = -sinθ = sin(-θ)

a - ib

= cos(-θ) + i sin(-θ)

Hence Conjugate of the complex number  cos θ + i sin θ​  is cos(-θ) + i sin (-θ​)

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