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## Simplifying Complex Numbers

#### High School - HSN-CN.A.1

How to Simplify Complex Numbers? One of the most common forms of number systems that students have to deal with is the complex numbers. These are numbers that are a combination of imaginary and real numbers. Real numbers include all rational and irrational numbers. An imaginary number is any negative integer in square root. Addition or Subtraction of Complex Numbers To add or subtract complex numbers, you identify the real and imaginary portion of the numbers and place the like terms together. Sum all numbers in the real portion and sum all numbers in the imaginary portion. You apply the same methodology when subtracting complex numbers. Multiplication of Complex Numbers To multiply complex numbers, you need to understand the F.O.I.L rule. F.O.I.L stands from first, outer, inner, last. You have to multiply each term of the first binomial with each term in the second binomial. Start by multiplying the first term of a binomial with the first term of the second one, multiply the same term with the second term of the second binomial. The third step is to multiply the second term of the first binomial with both terms of the second binomial. Simplify the sum further to get the final answer. Division of Complex Numbers Division of complex numbers is rather complicated, as compared to multiplication, subtraction, or addition. Write the division in the form of a fraction and multiply both the numerator and the denominator with the conjugate of the denominator. The conjugate of a complex number a+ib is a-ib It will help you convert the denominator from a complex number to a real number. These worksheets and lessons will show you how to simplify a series of complex numbers.