Complex Numbers and Solving Equations Honors Algebra II with Trig. Mr. Agnew

Essential Stuff Essential Question Essential Vocabulary How do you simplify expressions involving complex numbers? Essential Vocabulary Imaginary Number Complex Number Complex Conjugate

Imaginary Numbers Not all quadratic equations have real number solutions, so to overcome this problem, mathematicians created an expanded system of numbers using the imaginary unit 𝐢

Imaginary Unit, 𝒊 𝒊= −𝟏 𝒊 𝟐 =−𝟏 These properties allow us to simply the square root of a negative number.

Complex Numbers A complex number is a number that contains a real and an imaginary part. The standard form: 𝒂+𝒃𝒊 Real Imaginary

Add/Subtract/Multiply Add and Subtract Combine Like Terms Write in Standard Form Multiply FOIL Replace 𝒊 𝟐 with −𝟏 Combine Like Terms/Standard Form

Dividing with Complex Numbers Divide Multiply the numerator and denominator by the complex conjugate Complex conjugates are two complex numbers of the form: 𝒂+𝒃𝒊 and 𝒂−𝒃𝒊

The product of complex conjugates will always be a real number.

Homework Homework 5.5: Complex Numbers