#MathsInMinutes Day 19: i

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● i is a “number” used to represent the square root of -1.

● This otherwise unrepresentable concept is not really a number in the sense of counting, and is known as an imaginary number.

● The concept of I is useful when we are trying to solve an equation like x^{2} + 1 = 0, which can be rearranged as x^{2} = -1.

● Since squaring any positive or negative real number always gives a positive result, there can be no real number solutions to this equation.

● But in a classic example of the beauty and utility of mathematics, if we define a solution and give it a name (I), then we can reach a perfectly consistent extension of the real numbers.

● Just as positive numbers have both a positive and a negative square root, so -i is also a square root of -1, and the equation x^{2] +1 = 0 has two solutions.

● Armed with this new imaginary number, a new world of complex numbers, with both real and imaginary components, opens out before us.

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