
Introduction We know that the solution of a quadratic equation ax^{2} + bx + c = 0, a not equal to 01 with real coefficients a,b,c is given by real numbers x_{1} and x_{2} where x_{1} = b +Ö(b^{2}4ac)/2a x_{2} = b  Ö(b^{2}4ac)/2a only if the discriminant b^{2}  4ac >= 0. For b^{2}  4ac < 0, we do not have solution of equation 1 in the set of real numbers because square of every real number is nonnegative. The mathematical need to have solution for negative discriminant led us to extend the real number system to new kind of numbers, namely complex numbers that allow the square root of negative numbers. We assume that the square root of 1 is denoted by the symbol i, called imaginary unit. Thus, for any two real numbers a and b we can form a new number a+ib. This number a+ib is called complex number. The set of all complex numbers is denoted by C.
Complex Numbers
Example 1: Write the complex conjugate of 6i7
Example2: Write 4  Ö5 as a complex number.
Directions: Answer the following questions. Also write at least 5 examples of your own. 