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Published byKarlie Liford Modified over 2 years ago

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Complex Numbers

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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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