Simplifying Complex Fractions Online Tutoring Maths Help

Simplifying Complex Fractions Online Tutoring Maths Help 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.