Download 2.4 Complex Numbers Objectives: learn how to write complex

2.4 Complex Numbers
Objectives: learn how to write complex numbers, add, subtract, multiply, and divided complex numbers
Imaginary unit= i , i^2 = -1, and √-1 = i.
Complex numbers are in the form a + bi, containing a real number part (a) and an imaginary part (bi)
Adding Complex Numbers- treat the i’s like x’s and combine like terms. (3 – i) + (2 + 3i), 2i + (-4 – 2i)
Subtracting Complex Numbers- distribute the negative first. 3 – (-2 + 3i) + (-5 + 1), (3 + 2i) + (4 – i) – (7 +
i)
Multiplying Complex Numbers- multiply as normal, but remember i^2 = -1
4(-2 + 3i)
i(-3i)
(2 – i)(4 + 3i)
(3 + 2i)(3 – 2i)
(3 + 2i)^2
Dividing Complex Numbers: can’t have i as a denominator- multiply by the complex conjugate (the
opposite sign), complex conjugate of 4 + 2i is 4 – 2i, of -3i is 3i- causes i to cancel.
Divide 1/(1 + i)
Divide 2 + 3i/(4 – 2i)
Complex Solutions of Quadratic Equations
Reminder- you can only multiply what’s inside a square root (√2√3 = √6), can only add and subtract if the
radical is the same (2√5 + 8√5 = 10√5), remember to bring out i anytime there’s a negative inside a
square root.
Write each in standard form √-3√-12 (show 3 x 12 and simplifying 12 first), √-48 - √-27, (-1 + √-3)^2 foil
Solve each: x^2 + 4 = 0, 3x^2 – 2x + 5 = 0, 2x^2 – 5x + 7 = 0
Homework: 6 – 68 evens