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Vocabulary
Complete the chart.
Word  Definition 
_______________ 
Any number with an 
Complex Number  _____________________________________________ 
_______________ 
An imaginary number without a real part, only 
Simplifying the Radical  _____________________________________________ 
Discriminant  _____________________________________________ 
_______________  a complex number that, when used as an input ( x ) value, results in an output (y ) value of zero 
_______________  binomial terms which are equal aside from inverse operations between them, 
Complex Conjugates  _____________________________________________ 
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What does
What form do complex numbers have? _______________
What is the discriminant used for? ___________________________________________
Imaginary Numbers
Powers of
.
Simplify.

−25−−−−√ 
−19−−−−√ 
4−27−−−−−√ 
i3 
1723 
i148 
(0.2+1.5i)−(−0.6+i)
Multiply.

3i3⋅4i7 
4−75−−−−√⋅8−6−−−√ 
3−13−−−−√⋅11−21−−−−√
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Quadratic Formula and Complex Sums
The discriminant is used to determine how many roots a quadratic function has.
If b 2  4 ac > 0 then there are two unequal real solutions.

If b 2  4 ac = 0 then there are two equal real solutions.

If b 2  4 ac < 0 then there are two unequal complex solutions.


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Solve each equation and express the result as a complex number.

12x45x=315x2+16 
3x2−6x+15=0 
8x2−5x+11=0  When the sum of 4 + 8i and 2  9i is graphed, in which quadrant does it lie?
 If
z1=−3+2i andz2=4−3i , in which quadrant does the graph of(z2−z1) lie?  On a graph, if point A represents
2−3i and point B represents−2−5i , which quadrant containsA−B ?
Products and Quotients of Complex Numbers
Multiplying Complex Numbers
Multiply as you normally would without imaginary numbers, then deal with the
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Dividing Complex Numbers
Divide also as you would rational numbers. Remember that the procedure was to find the irrational conjugate of the denominator and then multiply both the numerator and the denominator by that conjugate. Because in complex numbers you want to elliminate the complex numbers from the denominator, you find the complex conjugate of the denominator and multiply BOTH the numerator AND the denominator by it.
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Multiply the complex numbers.

(4i−7)(12i3+3) 
(14−9−−−√)⋅(8−4−−−√) 
(16−1−−−√)⋅(21−81−−−−√)
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Divide the complex numbers.

4i2+4−6i2−1 
5i2−5−8i2+3 
−4−60−−−−√−2−20−−−−√
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