Presentation on theme: "5.3 Complex Numbers; Quadratic Equations with a Negative Discriminant."— Presentation transcript:
5.3 Complex Numbers; Quadratic Equations with a Negative Discriminant
Complex numbers are numbers of the form a + bi, where a and b are real numbers. The real number a is called the real part of the number a + bi; the real number b is called the imaginary part of a + bi.
(a + bi) + (c + di) = (a + c) + (b + d)i (2 + 4i) + (-1 + 6i) = (2 - 1) + (4 + 6)i = 1 + 10i Sum of Complex Numbers
(a + bi) - (c + di) = (a - c) + (b - d)i (3 + i) - (1 - 2i) = (3 - 1) + (1 - (-2))i = 2 + 3i Difference of Complex Numbers
Discriminant of a Quadratic Equation is called a discriminant >0, there are 2 unequal real solutions. =0, there is a repeated real solution. <0, there are two complex solutions. The solutions are conjugates of each other.