# Simplifying Complex Fractions

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Simplifying is a method to reduce or simplify a given expression to simpler form. Complex numbers are non-real numbers which are undefined on the number line. A complex number is of the general form a + bi, where ‘a’ is the real part of the complex number and ‘b’ is the imaginary part of the complex number. Here ‘i’ is the representation of the imaginary numbers and has a condition of i2 = -1. A complex number written in the p/q form is called as complex fractions.

Example 1: Simplify the complex number fraction 5 / (3 + i)?

Solution: Given is the complex number fraction 5/(3 + i)

Here the complex fraction has 5 in the numerator and (3 + i) in the denominator.

To simplify multiply the numerator and denominator with the conjugate of the complex number (3 + i) which is (3 – i).

This gives 5 (3 – i)/ (3 + i) (3 – i) = (15 – 5i) / [(9 – i2)] = (15 – 5i) /10

Hence the solution is 3/2 – i/2.

Example 2: Simplify the complex number fraction 6/ (2 + i)?

Solution: Given is the complex number fraction 6 / (2 + i)

Here the complex fraction has 6 in the numerator and (2 + i) in the denominator.

To simplify multiply the numerator and denominator with the conjugate of the complex number (2 + i) which is (2 – i).

This gives 6 (2 – i)/ (2 + i) (2 – i) = (12 – 6i) / [(4 – i2)] = (12 – 6i) /5

Hence the solution is 12/5 – 6i/5.