UNIT 3  : QUADRATIC FUNCTIONS & EQUATIONS

LESSON 7:  COMPLEX NUMBERS PART 2

Operations with Complex Numbers:

Definition:

The Complex Number system is the union of the set of all Real Numbers with the set of all Imaginary numbers (contain “i” factor)

It is defined formally as follows:

Complex numbers are added and subtracted just like any other variable in ordinary algebra –COMBINE LIKE TERMS.

Example 1:

Solution:

Note that in #d, the complex numbers are conjugates and their sum is a real number.

Multiplication &Division:

Again proceed as in ordinary algebra.  Replace any value of  i2 with (-1) .

Example 2:

Solutions:

Complex Conjugates:

.

Example 3:

Note that in all cases the product of a complex number and its conjugate is a real number.

Example 4:

When dividing complex numbers, multiply the numerator and denominator by the conjugate of the denominator.

Note that in all cases the quotient of two complex numbers is again a complex number.