We know that the solution of a quadratic equation
ax2 + bx + c = 0, a not equal to 0-------------1
with real coefficients a,b,c is given by real numbers x1 and x2 where
x1 = -b +Ö(b2-4ac)/2a
x2 = -b - Ö(b2-4ac)/2a
only if the discriminant b2 - 4ac >= 0.
For b2 - 4ac < 0, we do not have solution of equation 1 in the set of real numbers because square of every real number is non-negative.
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.
Example 1: Write the complex conjugate of -6-i7
Example2: Write 4 - Ö-5 as a complex number.
Directions: Answer the following questions. Also write at least 5 examples of your own.