Example 1.1.9 (b): Algebra with complex numbers

Simplify (1-2i)(1-2i)/(3i-4)
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Here the problem is to simplify the denominator (3i-4). The trick is to multiply top and bottom by 1, expressed as (-3i-4)/(-3i-4). The expression (-3i-4) is what will later be called the conjugate of (3i-4). That trick uses the general fact that

(a + ib) (a - ib) = a2 - iab + iab - i2 b2 = a2 + b2

where (a + ib) and (a - ib) are again called conjugate (as defined later). Anyway, using this trick the original expression simplifies considerably:


Interactive Complex Analysis, ver. 1.0.0
(c) 2006-2007, Bert G. Wachsmuth
Page last modified: May 29, 2007