Math is about to get imaginary!

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Presentation transcript:

Math is about to get imaginary! Complex Numbers Math is about to get imaginary!

Imaginary Numbers

Simplify imaginary numbers Remember 28

Answer: -i

Complex Numbers: A little real, A little imaginary… A complex number has the form a + bi, where a and b are real numbers. a + bi Real part Imaginary part

Adding/Subtracting Complex Numbers When adding or subtracting complex numbers, combine like terms.

Try these on your own

ANSWERS:

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

Lets do another example. F O I L Next

Answer: 21-i Now try these:

Next

Answers:

Now it’s your turn!

Do Now What is an imaginary number? What is i7 equal to? Simplify: √-32 *√2 (5 + 2i)(5 – 2i)

The Conjugate Let z = a + bi be a complex number. Then, the conjugate of z is a – bi Why are conjugates so helpful? Let’s find out!

We get Real Numbers!! The Conjugate = a2 + abi – abi –(bi)2 What happens when we multiply conjugates (a + bi)(a – bi) F O I L = a2 + abi – abi –(bi)2 = a2 – (bi)2 = a2 – b2i2 = a2 – b2(-1) = a2 + b2 We get Real Numbers!!