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MATH 1100 SECTION 3.4 Notes Complex Numbers – Text Pages 164-169 Complex Numbers: A complex number is a number written in the form a bi where a, b are real numbers, and i 2 1 (i.e, i 1 ). a is called the real part of the number, and b is called the imaginary part of the number. Examples: 2 3i , 1 3 i , 9i , 11 2 4 Adding, Subtracting and Multiplying Complex Numbers: a bi c di a c b d i a bi c di a c b d i a bi c di ac bd ad bc i Example 1: Express the following in the form a bi , by simplifying. (a) 7 6i 3 7i (b) 4 i 2 5i (c) 2 1 12i 24i 3 6 Example 2: Simplify. (a) i 24 (b) i 103 (Remember: i 2 1 ) Dividing Complex Numbers: a bi a bi c di ac bd bc ad i c di c di c di c2 d 2 Example 3: Simplify. (a) (b) 5i 3 4i 1 2i 3 i 2i Square Root of a Negative Number: If –r is negative, then the principle square root of –r is, r i r The two square roots of –r are, i r and i r . Example 4: Simplify. (a) (b) 9 4 1 1 1 1 Example 5: Find all solutions of the equation and express them in the form a bi , by simplifying. x 2 2x 2 0 (a) (b) z4 12 0 z