Understanding Complex Numbers and Their Properties
This comprehensive guide covers the fundamentals of complex numbers, including definitions and properties. It explains the concept of imaginary numbers, the use of complex conjugates for simplification in division problems, and how to represent complex numbers in the form a + bi, where "a" is the real part and "bi" the imaginary part. The notes also include techniques for solving equations and simplifying expressions involving complex numbers, along with charts comparing rational, irrational, and imaginary numbers. Additionally, it explores roots of functions involving complex numbers.
Understanding Complex Numbers and Their Properties
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Presentation Transcript
Imaginary/Complex Numbers Complex Conjugates Notes 5.7
Notes 5.7 Given the fact i2 = ________ The imaginary number is _____ which equals _____ Complex numbers are written in the form: _______________ Where “a” is a real number and bi is an imaginary number Simplify expression vs. Solving equation
Complete the chart about roots Rational Irrational Imaginary Irrational Rational Imaginary
Simplify numbers with imaginary numbers -1 -i 1 -i 1
Complex numbers are written in the form: ___________ Where a is a real number and bi is an imaginary number The complex conjugate is _____________ We will use complex conjugates to simplify division problems where a ______________ _________________ is in the denominator complex number
Operations with imaginary/complex numbers The 2nd problem shows complex conjugates being multiplied
Division with imaginary/complex numbers Multiply by a form of 1
Division with imaginary/complex numbers Multiply by a form of 1
Is 5+i a solution (root/zero) of the function f(x) = x2 – 10x + 26 ? YES,5+i is a root
