This section of my web site was in part inspired by my late brother Bill (William Fenwick Littlefair Simpson). When helping his grandson with mathematics he had rung me up and asked why is a minus times a minus a plus. I knew it was so and could demonstrate that it was so but I was never satisfied with the depth of the explanation I gave him.
Sometime later Bill came to my house. He had now encountered imaginary numbers when aiding his grandson and he was understandably highly sceptical saying the idea was crazy and that there could be no such things and that all numbers are real. I, in my engineering training had repeatedly done calculations with imaginary numbers and could only argue that they worked and gave satisfactory results.
Bill’s arguments set me thinking and if you read my blog on operators you will discover, as I did, that Bill was right and that there are no such things as imaginary numbers. It isn’t as if we are giving pupils a simpler version which they can understand and which can be expanded on. No, we are misleading them and those who go on to use such things in their work may never understand. We spend vast sums on often meaningless research projects. Wouldn’t it warrant just a little being spent on correcting our teachings and improving understandings.