A short history of complex imaginary numbers.

Intellectual property for solving equations was guarded in the 16th century.Calculating the behavior of projectiles in flight was of particular interest to ballistics and fortifications expert Niccolo Tartaglia.The x2 and x3 terms in the equations ring a bell with you from school.The problem lies in the fact that some solutions require the square roots of negative numbers.Negative numbers don't have square roots because there is no number that gives a negative number.When negative numbers are combined, they yield a positive result.

If they allowed negative square roots in their calculations, they could still give valid numerical answers.When he was beaten by one of Cardano's students in a month-long equation-solving duel in 1530, he learned this the hard way.

The square root of minus one is represented by i.The imaginary unit is not a real number and does not exist in real life.It can be used to find the square roots of negative numbers.I can say that -4 is 4 -1 if I want to calculate the square roots.The square root of -4 is the same root as the one of -1.In symbols.

The answer is that the square root of -4 is 2i.For the reasons stated above, -2 is a square root of 4.The square roots of -4 are 2i and -2i.

The math of i was an issue for mathematicians.We are innately familiar with the idea that a positive times a negative and that is why I stated above.With the imaginary unit, there are two positives and two negatives.

Some people felt that using them in formal mathematics was not rigorous because of this problem.In 1572, the Italian renaissance man, Rafael Bombelli, wrote a book called, simply, Algebra, where he tried to explain mathematics to people without degree-level expertise, making him an early educational pioneer.The case that the imaginary unit was neither positive nor negative and therefore did not obey the usual rules of arithmetic was made in his book.

The work of these mathematicians allowed the development of what is now called the Fundamental Theorem of Algebra.The highest power of the unknown in the equation is equal to the number of solutions to an equation.When I was working out the square roots of -4 above, I solved the equation x2Two is the highest power of the unknown x in the equation, and we found two answers, 2i and -2i.

If the highest power is three, I should get three solutions.The same form of equation that Tartaglia dealt with is called x3 + 4x.x is a solution of the equation.What about the other two solutions?

There are no real solutions to the equation, but there are imaginary ones.2i and -2i are two of the three solutions to this equation.

It wasn't until a few hundred years after Bombelli that the fundamental theorem of algebra was proven.The concept of complex numbers was pioneered by Argand.

There is an imaginary part and a real part to complex numbers.A complex number with a real part and an imaginary part is called 4 + 2i.Real numbers and imaginary numbers are both complex numbers.For example, 17 is a complex number with a real part equal to 17 and an imaginary part not equalling zero, and the same is true for the other number.

Abraham de Moivre was one of the first to relate complex numbers to geometry with his theorem of 1707.Argand diagrams are like a normal graph with an x and y axis, except his axes are the real and imaginary numbers.Complex problems were solved using geometry.

Until the modern electronic age, all of this was a purely academic interest.Audio signals for music and voice communication and alternating current power supplies are some of the things that are analysed using complex numbers.Complex numbers are important in understanding this strange world that has allowed us to enjoy modern computers, fibre-optics, gps, and more.From 500 years ago to the present day, mathematicians decided that imaginary numbers were worth investigating.

Our latest special editions cover a range of fascinating topics from the latest scientific discoveries to the big ideas explained.

Some of the best names in science and technology talk about their work.