The subject of complex eigenvalues brings up in me the emotionally disturbing subject of imaginary and complex numbers. | can still feel a little of my earlier anxiety. The episode started benignly enough. Our high school’s freshman algebra class was studying how to solve quadratic equations, equations in which the highest power of an expression was two. Told to work at the blackboard in front of the class, | was given the problem of finding the two values of x that were the
roots of the equation, 5x? + 3x + 4 = 0. | had been taught to use the memorized
_ + af 2 quadratic formula, rs in which a = 5, b = 3 and c = 4. | always a
calculated the square root part first and wound up with the expression,
/9—80 =J/-71.| can still feel the sinking feeling in my stomach as | looked at the result. | anticipated the usual snide remarks and embarrassment as | contemplated doing what | did not know how to do, take the square root of a negative number. Mr. Kirby, the retired mechanical engineer who was my high school freshman algebra teacher tried to help, but | did not trust him. It seemed to me that he had already humiliated me in front of the class, several times. He asked, “... what number when squared, multiplied by itself, would equal —7.” He then asked it another way: solve
the following equation for x: x°+1 = 0. Seeing something | could do, | wrote the next
line quickly x° = -7 and then, taking the square root of both sides, | wrote x = V-1.
He then asked me what that meant. | answered by writing quickly, glibly and blindly
that that meant that J—1xV/—1=-1. He asked me to explain what that meant by giving him an example from the real world. Not yet knowing about imaginary and complex (combine real and imaginary numbers), | stood head down, ashamed and silent, thinking that my smart friend Jerry Blau would get the answer immediately. Mr. Kirby said he would go on with the class while | continued to stand in front of the blackboard and thought about it. He told me to interrupt him when | was ready to answer. Some classmates were smirking, others giggled aloud. They had seen him do this to me before.
Mr. Kirby, a short, muscular man, an ex-marine with a military haircut and a brusque manner, lectured that mathematical competence and obedience to
authority and class discipline were all of a piece. | asked him about mathematical
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