Question

Evaluate (5 + i) . (3 + 2i)
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Answer 1

$\color{voilet}{Answer :}$

$\frac{5 + 2i }{3 + 2i} \: \: \frac{3 - 2i}{3 - 2i} \: = \frac{11 - 16i}{13} = \frac{11}{13} - \frac{ 16}{13} i$

$\color{yellow}{Explanation :}$

Dividing complex numbers is actually simpler than it seems. We don't start by dividing, rather we multiply the top and the bottom by the complex conjugate of the denominator. Remember that a complex number times its complex conjugate gives an entirely real number. Also, a fraction multiplied by anything in both the numerator and denominator is unchanged.

The complex conjugate of a complex number is obtained by flipping the sign on the imaginary portion. Let's begin!

$\frac{5 + 2i }{3 + 2i} \: \: \frac{3 - 2i}{3 - 2i} \: = \frac{11 - 16i}{13} = \frac{11}{13} - \frac{ 16}{13} i$