IMAGINARY AND COMPLEX NUMBERSHigher Concepts of MathematicsImaginary numbers are added or subtracted by writing them using the imaginary unit i and thenadding or subtracting the real number coefficients of i. They are added or subtracted likealgebraic terms in which the imaginary unit iis treated like a literal number. Thus, and259are added by writing them as 5i and 3i and adding them like algebraic terms. The result is 8iwhich equals or . Similarly, subtracted from equals 3i subtracted8164925from 5i which equals 2i or or . 214Example:Combine the following imaginary numbers:Solution:16 36 49 116 36 49 14i 6i 7i i10i 8i2iThus, the result is 2i 21 4Imaginary numbers are multiplied or divided by writing them using the imaginary unit i, and thenmultiplying or dividing them like algebraic terms. However, there are several basic relationshipswhich must also be used to multiply or divide imaginary numbers.i^{2}= (i)(i) = = -1(1 ) (1 )i^{3}= (i^{2})(i) = (-1)(i) = -ii^{4}= (i^{2})(i^{2}) = (-1)(-1) = +1Using these basic relationships, for example, equals (5i)(2i) which equals 10i^{2}.(25) (4 )But, i^{2} equals -1. Thus, 10i^{2} equals (10)(-1) which equals -10.Any square root has two roots, i.e., a statement x^{2} = 25 is a quadratic and has roots x = 5 since +5^{2} = 25 and (-5) x (-5) = 25.MA-05 Page 12Rev. 0

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