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Published byAlonso Hodgetts Modified over 3 years ago

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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

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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

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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.

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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

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Perform the indicated operation: (7 – 3i) + (4 + 5i) (2 – i) – (8 + 3i)

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(2 + 3i)(5 – i)

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The complex conjugate of the complex number z = a + bi is a - bi

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Write the complex number in standard form:

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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.

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Solve x 2 + x + 1 = 0

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