Section 5.9.B Complex Numbers.

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Presentation transcript:

Section 5.9.B Complex Numbers

Def: A complex number is any number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit. a + bi Real part Imaginary part Some answers can be just the imaginary part

The Complex Number System (a + bi) real numbers (b = 0) imaginary numbers (b ≠ 0) rational numbers irrational numbers pure imaginary (a = 0) non-pure imaginary (a ≠ 0)

Def: Two complex numbers are equal if their real parts are equal and if their imaginary parts are equal 10.) Solve for x and y 3x + 10i = 12 + 5yi Set real parts equal and imaginary parts equal then solve real imaginary 3x = 12 10i = 5yi x = 4 10 = 5y y = 2

add the imaginary parts Adding and Subtracting Complex Numbers Add the real parts and add the imaginary parts 11.) Add: (2 + 3i) + (6 - 4i) 12.) Subtract: (9 - 3i) - (6 + 2i)

http://www.youtube.com/watch?v=htiloYIILqs 13.) Multiply 2i(5i2 + 3i) Multiplication of imaginary numbers http://www.youtube.com/watch?v=htiloYIILqs 13.) Multiply 2i(5i2 + 3i) = 10i3 + 6i2 = 10•i2•i + 6i2 Replace the i2 with -1 = 10(-1)i + 6(-1) Standard form a + bi = -6 -10i

14.) Multiply: -3i(5 + 4i) but….. i2 = -1 15.) Multiply: (3 - 2i)(-1 + 3i)

16.) Multiply by the conjugate: FOIL

In-class assignment Homework Practice 5-9 Problems: 9-24 all Page 315 # 40 - 48 all Homework