Presentation on theme: "You will learn about: Complex Numbers Operations with complex numbers Complex conjugates and division Complex solutions of quadratic equations Why: The."— Presentation transcript:
You will learn about: Complex Numbers Operations with complex numbers Complex conjugates and division Complex solutions of quadratic equations Why: The zeros of polynomials are complex numbers
Imaginary unit Complex number Real part Imaginary part Standard form Imaginary number Equal Additive identity Additive inverse Complex conjugate Multiplicative identity Multiplicative inverse (reciprocal) Discriminant
A complex number is any number that can be written in the form: a + bi, where a and b are real numbers a is the real part and b is the imaginary part a + bi is called the standard form.
If a + bi and c + di are complex numbers then, Sum: a + bi + c + di = (a + c) + (b + d)I Difference: a + bi - c + di = (a - c) + (b - d)i
The complex conjugate of the complex number z = a + bi is a - bi
Write the complex number in standard form:
For a quadratic equation ax 2 + bx + c = 0 where a, b, and c are real numbers and a 0: If b 2 – 4ac > 0 there are two distinct real solutions. If b2 – 4ac = 0 there is one repeated solution. If b2 – 4ac < 0 there is a complex conjugate pair of solutions.