Solve the equation. 1.) 3x = 23 2.) 2(x + 7) 2 = 16 Warm Up
4.6 Perform Operations with Complex Numbers, part 1 Algebra II
Perform operations with complex numbers. Objective
Imaginary unit i – i = √-1. Note that i 2 = -1. Complex number – in standard form, a number a + bi where a and b are real numbers, a is the real part and bi is the imaginary part Imaginary number – if b ≠ 0 then a + bi. If a = 0 and b ≠ 0 then a + bi is a pure imaginary number. Vocabulary
Solve 2x = -72. Example 1 – Solve a quadratic equation
To add (or subtract) two complex numbers, add (or subtract) their real parts and their imaginary parts separately. Sum of complex numbers: (a + bi) + (c + di) = (a + c) + (b + d)i Difference of complex numbers: (a + bi) – (c + di) = (a – c) + (b – d)i Sum and Differences of Complex Numbers
Write the expression as a complex number in standard form. A.) (12 – 11i) + (-8 + 3i) B.) (15 – 9i) – (24 – 9i) C.) 35 – (13 + 4i) + i Example 2 – Add and subtract complex numbers
Write the expression as a complex number in standard form. A.) -5i(8 – 9i) B.) (-8 + 2i)(4 – 7i) Example 3 – Multiply complex numbers
Pg. 279 (3 – 19 first 2 columns) Assignment