By Alder.

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**Extra resources for An Introduction to Complex Analysis for Engineers**

**Example text**

Now look at the vertical line which is on the Y-axis. These are the points: fiy : 0 y 2g 42 CHAPTER 2. 10: A vertical strip If you square iy you get y 2 , and if 0 y 2 you get the part of the X axis between 4 and 0. So the left and bottom edges of the strip have been straightened out to both lie along the X-axis. We now look at the opposite edge, the points: f1 + iy : 0 y 2g We have (1 + iy)(1 + iy) = (1 y2) + i(2y) and if we write the result as u + iv we get that u = 1 y 2 and v = 2y .

The simplest answer is `well it jolly well ought to be', but if you take z = 1 and square it and then take the square root, there is no particular reason to insist on taking the positive value. On the other hand, suppose we adopt the convention that we mean the positive square root for positive real numbers, in other words, on the positive reals, square root means what it used to mean. Are we forced to take the negative square root for negative numbers? No, we can take any one we please. But suppose I apply two rules: 1.

McLachlan's book, [2], has lots of good applications and Esterman's [8] is a middle of the road sort of book which might suit some of you. It does the course, and it claims to be rigorous, using the rather debatable standards of the sixties. The book [9] by Jerrold Marsden is a bit more modern in approach, but not very dierent from the traditional. Finally, [10] by Ahlfors is a classic, with all that implies. There are lots more in the library; nd one that suits you. 1 (Alder's Law about Learning Maths) Confusion propagates.

### An Introduction to Complex Analysis for Engineers by Alder.

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