 # Section 2-5 Complex Numbers.

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Section 2-5 Complex Numbers

Section 2-5 complex numbers and i
operations with complex numbers (+,-, x) complex conjugates and division solving quadratic equations with complex solutions plotting complex numbers absolute value of complex numbers

Complex Numbers we learned back in Algebra 1 that the square root of a negative number is not a real number there is a way to work with these numbers using the imaginary unit, i we use this simple definition: for example:

Complex Numbers all numbers we work with are part of the set of complex numbers this set consists of all real numbers and all imaginary numbers (contain i) all complex numbers can be written in the form a + bi a is the real part, b is the imaginary part

Operations With Complex Numbers
to add complex numbers, add their like parts (same for subtraction) to multiply complex numbers, use FOIL use the fact that

Division of Complex Numbers
if a + bi is a complex number, then its complex conjugate is a – bi in order to simplify the division of two complex numbers, multiply the top and bottom of the fraction by the conjugate of the denominator use FOIL on both top and bottom; the bottom will no longer contain i

Solving Quad.’s now, when you solve a quadratic equation for which the discriminant is negative, you can find its complex solutions the solutions will be complex conjugates

Plotting Complex Numbers
complex numbers cannot be plotted on a single number line because they have both a real and imaginary part instead, we plot them on a complex plane which looks a lot like a coordinate plane we use for ordered pairs the axes of this plane are the real axis and the imaginary axis

Plotting Complex Numbers
a 3 – 6i

Absolute Value of Complex Numbers
remember that absolute value means distance from 0 on a number line for complex numbers, it’s the distance from the origin we use the distance formula to compute it