For any complex number  z,

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For any complex number  z,  the product   z z*  is a nonnegative real number:

z · z* = ( x + i y ) ( x – i y) = x2 – ( i y )2 = x2 + y2.

Therefore, the sum of squares of any real numbers can be factored into linear complex factors:

a2 + b2 = ( a + i b ) ( a – i b ).

The absolute value of  z  is denoted by the symbol  | z |  and defined as

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In order to divide a number by a nonzero complex number  z, multiply the number by the complex conjugate number  z*  and divide by the real number | z |2:

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Index Real Numbers Complex Numbers Exponentiation Algebraic Transformations Algebraic Equations and Ineualities Functions Discrete Algebra Basic Formulas Graphics of Basic Functions