Is there any number that, when multiplied by itself, equals Among the real numbers, the answer is no. However, the system of numbers can be expanded to include the imaginary unit defined as From this definition, it follows that which allows the square root of any negative number to be found. What results is called an imaginary number. Once replaces the negative sign, the square root of the remaining positive number can be evaluated as usual.
The set of complex numbers, represented by the symbol is formed by all numbers that can be written in the form where and are real numbers, and is the imaginary unit. Here, is called the real part and is called the imaginary part of the complex number.
Complex numbers can be added, subtracted and multiplied just like real numbers.
Simplify the following expressions.
Let's simplify the expressions, one at a time.