1-3 Imaginary Numbers.

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Presentation transcript:

1-3 Imaginary Numbers

in a math class far, far away.. A long long time ago, in a math class far, far away.. There was no way to take the square root of a negative number

Every time we squared a negative number We got a positive.

(-1) = 1 (-2) = 4 (-3) = 9

that when multiplied by itself Was there a number, that when multiplied by itself Gave you a negative???

Can we in fact, take the square root of a negative number? WE CAN!!!!

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It stretches the imagination.. I present to you:

So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary” So, does really exist?

Examples of how we use

Examples of how we use

Radicals and Fractions You can rearrange the radical sign. = reduce fraction first 10 2 = 5 OR separate first 25 36 = 25 36 = 5 6

Simplify

Powers of i

Simplify.

Complex Numbers Example: 5+4i Standard form is: Real part Imaginary part