Question

Write the conjugates of the following complex numbers:
i) $\sqrt{2}+\sqrt{3}i$
ii) cos θ + i sin θ

Answer 1

Answer:

i) √2 - i√3

ii) cos θ - i sin θ

Step-by-step explanation:

Hi,

If a + ib is any complex number such that a ∈R, b∈R  

and i = √-1,  

then the complex conjugate of a + ib is given by a - ib.

i) Conjugate of √2 + i√3

here a = 2 and b = √3

As we know the conjugate of a + ib is a- ib

Conjugate of √2 + i√3 is √2 - i√3

ii) Conjugate of cos θ + i sin θ

Here a = cos θ , b = sin θ and complex number is a + ib

Here , both a, b ∈ R,

So, Complex conjugate of a + ib

is a - ib

= cos θ - i sin θ

Hope, it helps !