Find the conjugates of the complex numbers $$\dfrac{(1 + i) (2 + i) }{ (3 + i)}$$

Asked by Aaryan | 1 year ago |  46

##### Solution :-

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

Let us convert to standard form,

$$\dfrac{(1 + i) (2 + i)}{(3 + i)}$$

$$=\dfrac{1(2+i)+i(2+i)}{3+i}$$

$$=\dfrac{1+3i}{3+i}$$

$$=\dfrac{1+3i}{3+i}\times \dfrac{3-i}{3-i}$$

$$\dfrac{3}{5}+\dfrac{4i}{5}$$

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

So,

The conjugate of  $$\dfrac{3}{5}+\dfrac{4i}{5}$$

Answered by Aaryan | 1 year ago

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