Find the conjugates of the complex numbers $$\dfrac{ (3 – i)^2} {(2 + i)}$$

Asked by Aaryan | 1 year ago |  53

##### Solution :-

Since the given complex number is not in the standard form of (a + ib)

Let us convert to standard form,

$$\dfrac{(3-i)^2}{2+i}=\dfrac{3^2+i^2-2(3)(i)}{2+i}$$

$$=\dfrac{8-6i}{2+i}$$

$$\dfrac{8-6i}{2+i}\times \dfrac{2-i}{2-i}$$

$$\dfrac{8(2-i)-6i(2-i)}{2^2-i^2}$$

= 2 - 4i

We know the conjugate of a complex number (a + ib) is (a – ib)

So,

The conjugate of (2 – 4i) is (2 + 4i)

Answered by Aaryan | 1 year ago

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