Until now it was only discovered by scientists that irrespective of numbers being positive or negative when squared, the result is always positive. In the late 1500s, Italian scholar Rafael Bombelli discovered and mentioned in his book named ‘ algebra ‘ rules for using imaginary and complex numbers. Here it was discovered that when an imaginary number is squared it will produce negative results, which was against the normal rule laid by the ancient scholars. Complex numbers are an addition to real numbers on the number line and imaginary numbers. Complex numbers are in the form of a+bi where a and b are real and i =square root of -1. Complex numbers help us to solve polynomial equations.

First invention

Italian scholars at the time were publicly challenged to solve the cubic equations in the least amount of time. Solving it in minimum time was a matter of pride for those who used to aim for the post of professor in a prestigious university. High secrecy was maintained by scholars about their inventions and formulas. Rafael bombelli was successful in finding solutions to cubic equations independently without being dependent on methods of the Persian polymath Omar khayyam.

Explaining numbers

Rafeal bombelli laid down rules for solving problems on complex numbers. He used the terms such as plus of minus to denote positive imaginary unit and minus of minus to denote negative imaginary unit l. Rafeal provided a successful way of solving cubic equations.

Rafael read Cardano ars  Magna with great interest . His own work was a very clear invention of time.  He also investigated the arithmetic of negative numbers. He set out new rules for addition, subtraction and multiplying imaginary numbers. He stated

“Plus of minus multiplied by plus of minus makes minus”—meaning a positive imaginary number multiplied by a positive imaginary number equals a negative number: He also gave practical examples of application of these rules for solving cubic equations and also equations related to complex numbers.

Applying complex numbers

Imaginary and complex numbers were also added in sets of other numbers. American mathematician Nathan Jacobson established the bold capital C to signify the set of complex numbers, {a + bi}, where a and b are real and i = square root of -1.

Complex numbers help in solving polynomial equations easily. Complex numbers were also useful in other branches of number theories.


The era in which complex and imaginary numbers came into existence as a part of algebra was from around 1500-1680. These numbers gave rise to irrational numbers which had an undefined value and could only be valued in √ or decimals form with the use of variables defining an imaginary value in mathematical terms.