Adding Complex Numbers
Subtracting Complex #'s
Multiplying Complex #'s
Solving Quadratic Equations with Complex Solutions
100
How do you add complex numbers?
Add like terms, both real and imaginary numbers
100
Is adding and subtracting complex numbers very similar?
Yes
100
What does FOIL stand for?
"Firsts, Outers, Inners, Lasts"
100
What are negative square roots called?
Complex roots
200
What is the sum of 3+i and -1+2i
2+3i
200
How do you subtract 2+3i from 4+7i?
(4 + 7i) − (2 + 3i) = 4 + 7i − 2 − 3i
= 4 − 2 + 7i − 3i
= 2 + 4
200
How do you multiply 3 + 2i by 1 + 7i?
= 3×1 + 3×7i + 2i×1+ 2i×7i
= 3 + 21i + 2i + 14i2
= 3 + 21i + 2i − 14 (because i2 = −1)
= −11 + 23i
200
What is an example of a non factor-able equation being solved?
300
Is i real or imaginary?
imaginary
300
How do you subtract 7-3i from 5+6i?
(5 + 6i) − (7 − 3i) = 5 + 6i − 7 + 3i
= 5 − 7 + 6i + 3i
= −2 + 9i
300
What is an example of FOIL?
Firsts: a × c
Outers: a × di
Inners: bi × c
Lasts: bi × di
(a+bi)(c+di) = ac + adi + bci + bdi2
300
If a quadratic equation cannot be solved, what formula must be used?
Quadratic formula
400
What is i^2
-1
400
What is i equal to?
400
What is quicker than FOIL?
(a+bi)(c+di) = (ac−bd) + (ad+bc)i
400
If a graph does not touch the x-axis, what does this mean?
There are no real roots, they are imaginary (a ± bi)
500
What are the steps to adding 5+6i and 7-3i?
(5 + 6i) + (7 − 3i) = 5 + 6i + 7 − 3i
= 5 + 7 + 6i − 3i
= 12 + 3i
500
What is the standard form of complex numbers?
a+bi
500
What is an example of the new method?
(3 + 2i)(1 + 7i)
=(3×1 − 2×7) + (3×7 + 2×1)i
=−11 + 23i
500
How can you know if you answer will contain 0,1, or 2 roots?
two real roots- b2 - 4ac > 0
one real root- b2 - 4ac = 0
two complex conjugate roots- b2 - 4ac < 0