FIND SQUARE ROOTS PERFORM OPERATIONS WITH PURE IMAGINARY NUMBERS. PERFORM OPERATIONS WITH COMPLEX NUMBERS. 5.4 Complex Numbers.

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FIND SQUARE ROOTS PERFORM OPERATIONS WITH PURE IMAGINARY NUMBERS. PERFORM OPERATIONS WITH COMPLEX NUMBERS. 5.4 Complex Numbers

Properties of a Square Root How to simplify a square root.  Rewrite the radicand into prime factors.  Only pair(s) of prime factors can be move out of the radical.  Any pair(s) taken out of the radical are multiplied together and written in front of the radical.  Non-pair(s) are left under the radical and multiplied together.

Properties of Square Root Expressions How to simplify square roots multiplied together.  Rewrite each number into prime factors.  Find pairs of prime factors and variables to pull out in front of the radical.  All non-pairs get multiplied together under one radical symbol.  All numbers in front of radical are multiplied together, including any coefficients.

Properties of Square Root Expressions How to simplify the division of square roots.  Simplify the fraction if possible.  Rewrite the numerator into prime factors.  Rewrite the denominator into prime factors.  If a radical still exists in the denominator, then rationalize.

Square Roots of Negative Numbers

Simplifying imaginary numbers

Operations with Complex Numbers Complex number, a + b i Has a real number part(a) and an imaginary number part(b i ). Adding/subtracting complex numbers Combine like terms

Operations with Complex Numbers Multiplying complex numbers Multiply numbers and imaginary numbers. If the complex number is a binomial use the distributive property (FOIL) Simplify imaginary numbers and if needed combine like terms.

Operations with Complex Numbers Dividing complex numbers To simplify a complex fraction the denominator needs to be a real number  Multiply the fraction by a form of one  Choose the conjugate of the denominator as the form of one.

Methods to solve quadratic equations

Solving Quadratics using Square Root property