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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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Chapter 5.9 Complex Numbers. Objectives To simplify square roots containing negative radicands. To solve quadratic equations that have pure imaginary.

Chapter 5.9 Complex Numbers. Objectives To simplify square roots containing negative radicands. To solve quadratic equations that have pure imaginary.

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