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SFM Productions Presents:. Another sleep deprived 45 minutes in your Villa Walsh Pre-Calculus experience!. 2.4 Complex Numbers. Homework for section 2.4. p164 #9-19, 25-29, 35-39, 43-45, 51-57, 63-77. The imaginary unit: i. Solve, using real numbers: x 2 + 1 = 0.
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SFM Productions Presents: Another sleep deprived 45 minutes in your Villa Walsh Pre-Calculus experience! 2.4 Complex Numbers
Homework for section 2.4 p164 #9-19, 25-29, 35-39, 43-45, 51-57, 63-77
The imaginary unit: i Solve, using real numbers: x2 + 1 = 0 Mathematicians got tricky and created an expanded number system, which included: i. i is defined as follows:
Real numbers combined with multiples of this imaginary unit are known as the: Set of Complex Numbers The STD form of a complex number is: a + bi Real part Imaginary part
If b = 0, then a + bi is an imaginary number. If b = 0, then a + bi = a and a therefore is a real number. If a = 0, then a + bi = bi and bi therefore is a pure imaginary number. EVERY number can be written as a complex number. Example: 4 = 4 + 0i
Multiplication of complex numbers. Note: after foiling, if you have an i2, you must change it to a (-1) and multiply as needed. Examples
Complex conjugates and division Doing this is along the same line as rationalizing the denominator - it cleans up the denominator so that the denominator is areal, rational number.
Pull out the -1 first…THEN do whatever the math has you do. Complex Solutions of Quadratic Functions Example
The different powers of i …and so on.