Complex Numbers.

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Presentation transcript:

Complex Numbers

The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

The equation x2 + 1 = 0 has no real number solutions since any solution must be a number whose square is -1.

In the set of real numbers, all squares are nonnegative numbers because

In the set of real numbers, all squares are nonnegative numbers because

In the set of real numbers, all squares are nonnegative numbers because the product of any two positive numbers is positive

In the set of real numbers, all squares are nonnegative numbers because the product of any two positive numbers is positive

In the set of real numbers, all squares are nonnegative numbers because the product of any two positive numbers is positive & the product of any two negative numbers is positive

In the set of real numbers, all squares are nonnegative numbers because the product of any two positive numbers is positive & the product of any two negative numbers is positive

So we must define a number i so that

So we must define a number i so that

For any positive real number b

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Write the number as a product of a real number and the number i

Multiply

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Simplify

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Simplify

7.7 Numbers 1-68