Complexity Examples And Worksheet With Answers - Johnny Wolfe
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11Complexity Examples
1. Why complex numbers?
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Equation 1: x
- 1 = 0.
Equation 1 has two solutions, x = -1 and x = 1. We know that solving an equation in x is
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equivalent to finding the x-intercepts of a graph; and, the graph of y = x
- 1 crosses the
x-axis at (-1,0) and (1,0).
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Equation 2: x
+ 1 = 0
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Equation 2 has no solutions, and we can see this by looking at the graph of y = x
+ 1.
Since the graph has no x-intercepts, the equation has no solutions. When we define
complex numbers, equation 2 will have two solutions.
Complexity Johnny Wolfe
Jay High School Santa Rosa County Florida October 11, 2001
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