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Quadratic Functions

Quadratic Equations

Problems/Quadratic Functions

Problems/Quadratic Equations

Radicals

Complex Numbers 1

Complex Numbers 2

Reciprocal Functions

Review&Test

 

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UNIT 3 : QUADRATIC FUNCTIONS & EQUATIONS

 LESSON 7: COMPLEX NUMBERS PART 2

 

Operations with Complex Numbers:

 

Text Box:         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:

Text Box:

 

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 i2 with (-1) .

 

Example 2:

Solutions:

 

 

Complex Conjugates:

 

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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.

 

 

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