College Algebra Complex Numbers
Basic Definitions and Graphical Representation of Complex Numbers
   Concepts 1

Definition 1
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A complex number, z, is a number of the form z = x+iy where x and y are real numbers and .
Note: i2 = -1.

Definition 2
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For the complex number z=x+iy, the real numbers x and y are known as the real and imaginary parts of z , respectively, and denoted Re z=x, Im z=y.

Definition 3
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Two complex numbers z1=x1+iy1 and z2 = x2+iy2 are defined to be equal if and only if their real parts are equal and their imaginary parts are equal; that is, z1 =z2 if and only if x1= x2 and y1= y2.

Consequence. If the complex number x+iy=0, then x=0 and y=0.

Definition 4
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Let z=x+iy. Then the complex conjugate of z, denoted , is defined as =x-iy.

Frequently used formulas


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