Higher Concepts of Mathematics IMAGINARY AND COMPLEX NUMBERSExample 2:Multiply the following complex numbers:(3 + 5i)(6 - 2i)=Solution:(3 + 5i)(6 - 2i) = 18 + 30i - 6i - 10i2= 18 + 24i - 10(-1)= 28 + 24iExample 3:Divide (6+8i) by 2.Solution:68i26282i34iA difficulty occurs when dividing one complex number by another complex number. To getaround this difficulty, one must eliminate the imaginary portion of the complex number from thedenominator, when the division is written as a fraction. This is accomplished by multiplying thenumerator and denominator by the conjugate form of the denominator. The conjugate of acomplex number is that complex number written with the opposite sign for the imaginary part.For example, the conjugate of 4+5i is 4-5i.This method is best demonstrated by example.Example: (4 + 8i) ÷ (2 - 4i)Solution:48i24i24i24i832i32i2416i2832i32(1)416(1)2432i206585iRev. 0 Page 15 MA-05
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