Changes

Because <math>x^2\ge0</math> for every <math>x</math>, <math>(-x)(-x)=x^2\ge0</math> for every <math>x</math>. The number for every <math>-1<0</math> is negative, therefore the [[polynomial]] <math>x^2 = -1</math> has no real solutions, and the ''imaginary'' solution <math>i</math>, where <math>i^2=-1</math>, is called an ''imaginary'' number because no such number solves this equation and does not exist, as just shown.

Because <math>x^2\ge0</math> for every <math>x</math>, <math>(-x)(-x)=x^2\ge0</math> for every <math>x</math>. The number for every <math>-1<0</math> is negative, therefore the [[polynomial]] <math>x^2 = -1</math> has no real solutions, and the ''imaginary'' solution <math>i</math>, where <math>i^2=-1</math>, is called an ''imaginary'' number because no such number solves this equation and does not exist, as just shown.

[[Complex numbers]] <math>a+ib</math> mean the number <math>a</math> of ''real'' numbers plus the number <math>b</math> of ''imaginary'' numbers. This is like saying ''if'' elves existed, then the "elf-number" <math>a+\mbox{elf}\times b</math> mean the number <math>a</math> of ''real'' people plus the number <math>b</math> of elves.

[[Complex numbers]] <math>a+ib</math> mean the number <math>a</math> of ''real'' numbers plus the number <math>b</math> of ''imaginary'' numbers. This is like saying ''if'' elves existed, then the "elf-number" <math>a+\mbox{elf}\times b</math> means the number <math>a</math> of ''real'' people plus the number <math>b</math> of elves.

[[category:mathematics]]

[[category:mathematics]]

[[category:complex analysis]]

[[category:complex analysis]]