Section 4.6 Complex Numbers

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Presentation transcript:

Section 4.6 Complex Numbers

it is a symbol for a specific number Definition of pure imaginary numbers: i is not a variable it is a symbol for a specific number

Definition of pure imaginary numbers: Any positive real number b, where i is the imaginary unit and bi is called the pure imaginary number.

Simplify each expression.

Simplify each expression. Remember Remember

Definition of Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary unit.

Definition of Equal Complex Numbers Two complex numbers are equal if their real parts are equal and their imaginary parts are equal. If a + bi = c + di, then a = c and b = d

When adding or subtracting complex numbers, combine like terms.

Simplify.

Simplify.

Multiplying complex numbers. To multiply complex numbers, you use the same procedure as multiplying polynomials.

Simplify. F O I L

Simplify. F O I L

To divide complex numbers, multiply the numerator and denominator by the complex conjugate of the complex number in the denominator of the fraction. 7 + 2i 3 – 5i The complex conjugate of 3 – 5i is 3 + 5i.

7 + 2i 3 – 5i (3 + 5i) (3 + 5i) 21 + 35i + 6i + 10i2 9 + 15i – 15i – 25i2 11 + 41i 34 21 + 41i – 10 9 + 25