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

Asked by Aaryan | 1 year ago |  61

##### Solution :-

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

Let us convert to standard form,

$$\dfrac{(3 – 2i) (2 + 3i) }{ (1 + 2i) (2 – i)}=\dfrac{6+5i-6(-1)}{2+3i-2(-1)}$$

$$= \dfrac{12+5i}{4+3i}$$

$$\dfrac{12+5i}{4+3i}= \dfrac{12+5i}{4+3i}\times \dfrac{4-3i}{4-3i}$$

$$= \dfrac{63-16i}{25}$$

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

So,

The conjugate of $$\dfrac{ (63 – 16i)}{25}$$ is $$\dfrac{ (63 + 16i)}{25}$$

Answered by Aaryan | 1 year ago

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