ASMD Complex Numbers
Add. Write in standard form.
(4-3i) + (3-5i)
7-8i
Solve.
v2=144
v= 12, -12
What's the quadratic formula?
x=-b+sqrt(b2-4ac)/2*a
Suppose that the functions p and q are defined as follows.
p(x)=x2+7
q(x)=sqrt(x+4)
Find the following.
(p∘q)(5)
(q∘p)(5)
(p∘q)(5)=16
(q∘p)(5)=6
Name a school Professor Syvuk attended
Midpark, Case, OSU
Multiply. Write in standard form.
(2-3i)(1-4i)
-10-11i
Write in terms of i.
sqrt(-18)
3i*sqrt(2)
Solve for x.
3x2-6x-2=0
x= (6+sqrt(60))/6 , (6-sqrt(60))/6
OR
x= (3+sqrt(15))/3 , (3-sqrt(15))/3
Suppose that the functions u and w are defined as follows.
u(x)=2x
w(x)=x2+1
Find the following.
(w∘u)(−2)
(u∘w)(−2)
(w∘u)(−2)=17
(u∘w)(−2)=10
In what month was Professor Syvuk born?
March
Subtract. Write in standard form.
(-4+i) - (-5+3i)
1-2i
Solve for y.
-30y=9y2+25
-5/3
Find all complex solutions of 8x2+x+2=0
x= (-1/16)+(3sqrt(7)/16)i , (-1/16)-(3sqrt(7)/16)i
Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=x+3
s(x)=2x-1
Write the expressions for (r·s)(x) and (r+s)(x) and evaluate (r-s)(2).
(r·s)(x)=2x2+5x-3
(r+s)(x)=3x+2
(r-s)(2)=2
What was Professor Syvuk's first car?
Ford Focus
Multiply. Write in standard form.
-i(6+5i)
5-6i
Simplify the complex number i32 as much as possible.
1
A ball is thrown from a height of 40 meters with an initial downward velocity of 10 m/s. The ball's height h (in meters) after t seconds is given by the following.
h=40−10t-5t2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
t= 2.00 seconds
Suppose that the functions f and g are defined as follows.
f(x)=x/x-7 g(x)=2/x+9
Find f/g. Then, give its domain using an interval or union of intervals.
Simplify your answers.
(f/g)(x)=x(x+9)/2(x-7)
Domain of f/g: (−∞,−9)∪(−9,7)∪(7,∞)
What is Professor Syvuk's middle name?
Edward
Divide. Write in standard form.
6i/(-3+4i)
(24/25)-(18/25)i
Simplify the complex number i29 as much as possible.
i
The length of a rectangle is 5 yd less than double the width, and the area of the rectangle is 52 yd2. Find the dimensions of the rectangle.
Length: 8 yd
Width: 6.5 yd
Suppose that the functions f and g are defined as follows.
f(x)=2x+5
g(x)=sqrt(x-3)
Find f/g and f+g. Then, give their domains using interval notation.
(f/g)(x)=2x+5/sqrt(x-3)
Domain of f/g: (3,∞)
(f+g)(x)= 2x+5+sqrt(x-3)
Domain of f+g: [3,∞)
What is Professor Syvuk's favorite TV show from the 2000s?
Lost