The Algebra Prove the Complex Identity Standard Worksheet

40 pts3.06a Finding Standard Form by Completing the Square
Classify each as Circle, Quadratic (parabola) or other
(x − 5)2 + (y − 2)2 = 16
x2 + y 2 = 100
y 2 − x = 25
(x − 2)2 − (y + 5)2 = 10
y = 2x + 5
Complete the square to determine if the equation is a circle, quadratic (parabola) or other.
work and graph the circles and quadratics on a grid.
16×2 + 4y 2 + 96x − 8y + 84 = 0
x2 + y 2 + 8x − 6y − 15 = 0
x2 + 6x + 4y + 5 = 0
Show all
Show all steps to prove the complex identity. 10 points each
1. Show that (a + bi)2 = (a + b)(a − b) + 2abi
2. Show that (2x + i)(2x − i) = 4×2 + 1
3. Show that ( 1 + i)2 = 2i
5.03a assessment
Review the content for section 5.03a. Use the practice problems to show whether or not the rational
expressions are closed under the following operations. Upload your answers in the dropbox provided.
10 points each
1. Is the set of rational expressions closed under ​subtraction​? Explain
p(x)
q(x)
–
r(x)
s(x)
= ______________
2. Is the set of rational expressions closed under ​multiplication​? Explain
p(x)
r(x)
( q(x) ) ( s(x) ) = _______________
3. Is the set of rational expressions closed under ​division​? Explain
p(x)
q(x)
÷
r(x)
s(x)
= ________________