5 3 complex numbers quadratic equations with a negative discriminant n.
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5.3 Complex Numbers; Quadratic Equations with a Negative Discriminant

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5.3 Complex Numbers; Quadratic Equations with a Negative Discriminant. C. o. m. p. l. e. x. n. u. m. b. e. r. s. a. r. e. n. u. m. b. e. r. s. o. f. t. h. e. +. a. b. i. f. o. r. m. ,. w. h. e. r. e. a. a. n. d. b. a. r. e. r. e. a. l. n. u.

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slide3

Sum of Complex Numbers

(a + bi) + (c + di) = (a + c) + (b + d)i

(2 + 4i) + (-1 + 6i) = (2 - 1) + (4 + 6)i

= 1 + 10i

slide4

Difference of Complex Numbers

(a + bi) - (c + di) = (a - c) + (b - d)i

(3 + i) - (1 - 2i) = (3 - 1) + (1 - (-2))i

= 2 + 3i

slide7

Theorem

The product of a complex number and its conjugate is a nonnegative real number. Thus if z=a +bi, then

slide11

In the complex number system, the solution of the quadratic equation

where a, b, and c are real numbers and

are given by the formula

discriminant of a quadratic equation
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.