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Complex Numbers

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**The imaginary unit i is defined as**

Complex Numbers The imaginary unit i is defined as

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Example

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Complex Numbers The set of all numbers in the form a + bi with real numbers a and b, and i, the imaginary unit, is called the set of complex numbers. The real number a is called the real part, and the real number b is called the imaginary part, of the complex number a + bi.

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**Equality of Complex Numbers**

a+bi = c+di if and only if a = c and b = d

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**Adding and Subtracting Complex Numbers**

Multiplying Complex Numbers

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Example Simplify:

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Example Multiply:

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**Conjugate of a Complex Number**

The complex conjugate of the number a + bi is a - bi, and visa-versa. The product of a complex number and its conjugate is a real number.

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Example Rationalize:

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**Principal Square Root of a Negative Number**

For any positive real number b, the principal square root of the negative number -b is defined by

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Example Simplify:

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Quadratic Formula

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Examples Solve:

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5.6 Complex Numbers. Solve the following quadratic: x 2 + 1 = 0 Is this quadratic factorable? What does its graph look like? But I thought that you could.

5.6 Complex Numbers. Solve the following quadratic: x 2 + 1 = 0 Is this quadratic factorable? What does its graph look like? But I thought that you could.

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