Complex Numbers Worksheet Page 4

Math 96–Complex Numbers–page #4

Rationalizing Denominators. In the complex number system, you can never leave i in the

denominator. You need to rationalize the denominator by multiplying the fraction by a form of one.

When the denominator is a binomial, multiply both numerator and denominator by the conjugate of the

denominator. Observe.

becomes

Remember to reduce your result if possible. All three “numbers” reduce simultaneously (or you

can factor to reduce). The result

. Some books wri

aa.

. If you write this in a + bi form, you may need to reduce furth

Homework. Rationalize the denominators.

38.

39.

40.

41.

42.

Try rationalizing the denominators on the following:

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