WARM UP

Is x-2 a factor of x2 - x -2. verify using synthetic

division or long division.

MATH IV LESSON10 COMPLEX NUMBERS 2.4Essential Question: How do you perform operations with complex numbers?

Standard: MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

Complex number: a number composed of a real part and an imaginary part.

Standard form of a complex number: a + bi Pure imaginary number: bi Equality of complex numbers: if a + bi = c

+ di, then a = c and b = d Imaginary unit i: the square root of negative

one.

New Vocabulary

= i Imaginary numbers

• Simplify the following complex numbers

b.

A complex number has both an imaginary part and a real part, and is written in standard form a + bi

• Simplify the complex number

a. + 5

b. - 4

EQUALITY OF COMPLEX NUMBERS. IF TWO COMPLEX NUMBERS ARE EQUAL THEN THEIR CORRESPONDING PARTS ARE EQUAL.

If a + bi = c + di , then a = c, and b = d

Example problem: a + bi = -7 + 2iSolve for a and b

ADDING AND SUBTRACTING COMPLEX NUMBERS Example: (3-i) + (2 + 3i) (3-i) + (2 + 3i) = 5 + 2i

Combine like terms Example: (3 – i) – (2 + 3i) Distribute your negative sign to get3 – i – 2 – 3iThen combine like terms to get1 - 4i

MULTIPLYING COMPLEX NUMBERS

∙ =

Multiplying complex numbers continued

(2-i)(4 + 3i) =

COMPLEX CONJUGATESIf a complex number has the form a + bi Then its complex conjugate is a – bi

Example: Find the complex conjugate of 6 – 7i

(3-5i)(3+5i) =

Multiplying complex conjugates

GRAPHING COMPLEX NUMBERS

Graph: 3 + 5i 2 + 3iAnd1 -2i

Real axis

Imaginary axis

HOME WORK

P 138 # 1, 5, 15-19 odd, 25,29,37,38, 65,66