
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:
Addition
& Subtraction:
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 i^{2} 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.