Complex Numbers Add and Subtract complex numbers Multiply and divide complex numbers.

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Presentation transcript:

Complex Numbers Add and Subtract complex numbers Multiply and divide complex numbers

Lets solve x 2 = -1 To solve these problem, French mathematician René Descartes proposed that a number i be defined such that i 2 = -1.

Simplify No Decimals

Simplify No Decimals

Simplify No Decimals

Simplify No Decimals

Powers of i values go a in a circle Power of i are a cyclical function

Powers of i values go a in a circle Find the value the expression

Powers of i values go a in a circle Find the value the expression

Adding Pure imaginary numbers are like terms.

Multiply Imaginary Numbers Remember i 2 equals -1

Multiply Imaginary Numbers Pull the i out first

Multiply Imaginary Numbers Pull the i out first

Solve Remember when you take the square root of a number you must remember its positive and negative answer.

Complex number Have two parts: Real and Imaginary

When adding complex numbers, add the real numbers together and then the imaginary numbers.

When adding complex numbers, add the real numbers together and then the imaginary numbers.

When subtracting complex numbers, add the real numbers together and then the imaginary numbers.

When subtracting complex numbers, add the real numbers together and then the imaginary numbers.

When subtracting complex numbers, add the real numbers together and then the imaginary numbers.

Multiplying Complex numbers Its time to remember how to FOIL again.

Multiplying Complex numbers Its time to remember how to FOIL again.

Multiplying Complex numbers Its time to remember how to FOIL again.

Divide Complex numbers Complex Conjugate work as with real numbers conjugates.Important must break into fractions

Homework Page 274 #19 – 41 odd, 49 – 55 odd

Homework Page 274 #18 – 40 even, 48 – 54 even