VIEWS: 1,383 PAGES: 18 CATEGORY: Education POSTED ON: 11/7/2011 Public Domain
Complex Numbers Definition of pure imaginary numbers: Any positive real number b, 2 2 b b 1 bi where i is the imaginary unit and bi is called the pure imaginary number. Definition of pure imaginary numbers: i 1 2 i 1 i is not a variable it is a symbol for a specific number Simplify each expression. 1. 81 81 1 9i 2. 121x 121x 1 x 5 4 11 i x 2 x 3. 200 100 1 2x x 10i 2x Simplify each expression. 4. 8i 3i 24i 24 1 2 2 Remember i 1 24 5. 5 20 i 5 i 20 Remember that 1 i i 100 110 10 2 2 Remember i 1 i Cycle of "" i 1 0 i 1 4 i i 1 i i 5 i 1 2 i 1 6 i i 3 i i 7 Simplify. 12 To figure out where we i are in the cycle divide the exponent by 4 and look at the remainder. 12 4 = 3 with remainder 0 So i i 1 12 0 Simplify. 17 Divide the exponent by 4 i and look at the remainder. 17 4 = 4 with remainder 1 So i 17 i i 1 Simplify. 26 Divide the exponent by 4 i and look at the remainder. 26 4 = 6 with remainder 2 So i 26 i 1 2 Simplify. 11 Divide the exponent by 4 i and look at the remainder. 11 4 = 2 with remainder 3 So i i i 11 3 Definition of Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary unit. Definition of Equal Complex Numbers Two complex numbers are equal if their real parts are equal and their imaginary parts are equal. If a + bi = c + di, then a = c and b = d When adding or subtracting complex numbers, combine like terms. Ex: 8 3i 2 5i 8 2 3i 5i 10 2i Simplify. 8 7i 12 11i 8 12 7i 11i 4 18i Simplify. 9 6i 12 2i 9 12 6i 2i 3 8i Multiplying complex numbers. To multiply complex numbers, you use the same procedure as multiplying polynomials. Simplify. 8 5i2 3i F O I L 16 24i 10i 15i 2 16 14i 15 31 14i Simplify. 6 2i 5 3i F O I L 3018i 10i 6i 2 30 28i 6 24 28i