Presentation on theme: "Warm Up Simplify Solve SAT Review question"— Presentation transcript:
1 Warm Up Simplify Solve SAT Review question Dana walks from home to school at a rate of 5 mph. It takes her 2 hourslonger to walk home from school than it did to walk to school. If her totalwalking time to and from school was 8 hours, what was Dana’s rate ofspeed walking home from school?a) b) c) d) e) 15
2 Section 5.4 Complex Numbers Essential Question What is an imaginary number?
3 Imaginary UnitUntil now, you have always been told that you can’t take the square root of a negative number. If you use imaginary units, you can!The imaginary unit is i.i=It is used to write the square root of a negative number.
4 Property of the square root of negative numbers If r is a positive real number, thenExamples:
5 *For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead. Example:
12 ConjugatesThe conjugate of a complex number has the same real part and the opposite imaginary partEx. Find the conjugate of 5 + 3i5 – 3iEx. Find the conjugate of 3 – 2i3 + 2i
13 Imaginary numbers in the denominator i’s cannot be in the denominator (like radicals)To get rid of the i’s, multiply numerator and denominator by the conjugateIf there is only an imaginary part in the denominator, multiply by the same imaginary number