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Complex Numbers

Powers of i
Example 1 Simplify i2.
Example 2 Powers of i > 4

Complex Numbers
Example 1 Simplify square root or radical of a negative number and complex number involving the square root or radical of a negative number
 Example 2 Simplify complex number in numerator in radical form

Addition, Subtraction of Complex Numbers
Addition 1 Simplify q = (4 - 3i) + (5 - 7i)
 Subtraction 1 Simplify w = (4 - 3i) - (5 - 7i)

Multiplication of Complex Numbers
Example 1 Simplify (2i) * (7i)
 Example 2 Simplify (-5i)2
 Example 3 Simplify q = -3 i * (4 - 5 i )
 Example 4 Simplify q = (5 - 2i) * (3 + 4i)
 Example 5 Simplify w = (2 + i)*(2 - i)
 Example 6 Simplify q = (3 + i )2
 Example 7 Simplify u = (2 - 3i)2 + (2 - 3i)

Division of Complex Numbers
Example 1 Simplify complex numerator to be factored

Rationalize Denominator with Conjugate
Example 2 Simplify complex fraction, denominator to be rationalized
 Example 3 Simplify complex fraction, denominator to be rationalized
 Example 4 Simplify complex fraction, denominator to be rationalized; given via radicals

Complex Plane, or Argand Diagram
Example 1 Plot in the Complex Plane complex number to be plotted in the complex plane
 Example 2 Convert point in the complex plane: convert to a complex number in the complex plane to a complex number.

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