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Dovator [93]
3 years ago
5

Simplify 5+2i/6+i

Mathematics
1 answer:
nlexa [21]3 years ago
3 0

Given problem is \frac{(5+2i)}{(6+i)}

To simplify that we need to multiply and divide by conjugate of the denominator

conjugate of denominator 6+i will be 6-i as we just need to change sign of the imaginary part

Now multiply and divide by 6-i


=\frac{(5+2i)}{(6+i)}\cdot\frac{(6-i)}{(6-i)}

=\frac{30-5i+12i-2i^2}{36-6i+6i-i^2}

=\frac{30+7i-2i^2}{36-i^2}

=\frac{30+7i-2\left(-1\right)}{36-\left(-1\right)}

=\frac{30+7i+2}{36+1}

=\frac{32+7i}{37}

=\frac{32}{37}+\frac{7}{37}i

Hence final answer is \frac{32}{37}+\frac{7}{37}i

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