Thanks for the fast reply. So I haven't taken a math class since my junior year of high school and now I'm a junior in college so please forgive me with all these dumb questions. The problem is 3 + 4i, and I just need to convert it to re^itheta. I get r = 5, and tan(theta) = 4/3. How do I convert this value in terms of pi? You don't need to give solutions, just a guide in the correct thought process and procedure would be great! This is for my physical chemisty class btw. Our assignment says to not use calculators and to simply everything.

Okay, hopefully someone can explain this to me. It is about solving a system of equations for three equations. Here is the example in the book: 2x+y-z=2
x+3y+2z=1
x+y+z=2
Solution: Begin by eliminating the term with x, this time from equations 2 and 3 as follows.
2x+y-z=2
-5y-5z=0
-y-3z= -2
My question is how did the book arrive at the last two equations?? There are a couple more steps to solve the problem, but I have to understand the first step before I move on. If anyone could help I would greatly appreciate it.

Sounds like theta is required to be in radians is all, since there's 2pi radians in a circle. I don't know if there's some cute way of doing it, or if you simply do tan^-1(4/3) in radian mode on your calculator.

Thanks, looks like its just a preference issue. Would leaving the exponent as i(tan-1(4/3))pi suffice as theta? Is that a standard notation?

You're allowed to create new equations by

1) multiplying an old equation by a constant.
Idea: If Left Side = Right Side, then certainly
c*(Left Side) = c*(Right Side)

2) Adding two equations together (on both sides)
Idea: If A = B and C = D, then
A + C = B + D

So combining those ideas together, we can multiply an equation by a constant and add the resulting equation to an existing one. In the case above, we used this technique to cancel the x's in eqns #1 and #2.

Hope this helps.

-BW

yes

edit: lol that i had to wait to post this, since the forum requires > 25 seconds between posts. Seriously, I got flagged for that in a math homework help thread. FML.

edit #2 -- siegmund is right. you added an extra pi and I missed it. theta = arctan(4/3).

theta=arctan(4/3) may well be acceptable. Not the extra pi. arctan(4/3) is a number -- about .927 radians, or 53.1 degrees, or 0.295*pi radians.

It doesn't look like their intention is for you to search for a rational equivalent.

Just i(tan^-1(4/3)). Note that this form does not specify whether theta is to be considered in radians or degrees. They're just different units of measurement, like miles and kilometres. x degrees = x(pi/180) radians.

Yes, thanks for clearing this up for me.

Thanks everyone for the help. Helped out a lot since I had 15 of these problem to work out.

Cool problem from my math test today. I had about 10 minutes to do it.

How many integers between 0 and 10,000 have digits that sum to 13?

Why for small angles does sin(theta) = theta? Can someone explain the reasoning behind, or point to a website that can show some graph/pictures why? I remember something about pendulums and why we can use sin(theta) = theta for solving for variables in a pendulum problem but I don't have the slightest idea how to explain it, our physics professor just said assume sin(theta) = theta for small angles and never explain why in detail.

Also quick question...pretty simple one, just want to make sure if I am on the right track - lol first assignment with no lectures about it and its due tomorrow

Simplify: 2e^(3ln(2)) = (2e^3)(e^ln2) = (2e^3)(2) = 4e^3

Sound about right?

How much, if any, calculus do you know?

edit: the short answer is just -- graph y=x and y=sin(x), and see that they are very close near x=0. The longer answer can involve tangent lines, linearization, and/or Taylor series.

If this is referring to me, I took calculus in high school and never bothered to take it in college (always putting it off until next semeter haha, bad idea, forgot everything). That was about 5 years ago and I am retaking it because some medical schools require college calculus ldo. Btw, what I am working on is like a "warming up math skills" homework assignment, the class isn't a calculus class, just uses math to derive certain equations that we will end up using.

edit: Thanks for the help, I will look up some of the long answer hints you gave me and see if I can jog my memory.

No. a^(bc) = (a^b)^c = (a^c)^b, whereas a^(b+c) = a^b * a^c.

The tangent line is a local approximation to a curve. ie "Near" the point of tangency, the curve "looks like" the tangent line. The tangent line to y=sin(x) at x=0 is y=x, so "near 0", we can approximate sin(x) by x.

Ahh, ok thanks.

Ended up getting 2e^(3ln2) = 2e^ln(2^3) = 2e^ln8 = 16


Appreciate all the help.

How did you get that number? I left my answer in choose notation, and didn't add it up.

He's wrong. It's a tetrahedron with 4 corners chopped off.

561-81=480

=C(16,3)-4C(6,3)

As I said, it's a tetrahedron with 4 corners chopped off. DUCY?

lol -- I am teh suck at adding. Yes, clearly 480.

And yes, I see why, and I'm a touch embarrassed I didn't notice that sooner.

I did the math out, and I got to 480, but I don't quite understand the 4C(6,3) part. I had a much longer way to find a sum that adds up to 4C(6,3). I also don't understand the tetrahedron part. Would it be possible to explain this?

Thanks!

I am having trouble with this last problem in my homework set. The problem is

Integrate: e^(-4x^2)dx from -infinity to +infinity.

I tried looking up identities for integrating e^(-ax^2) but only managed to find one possible hopeful hint. I found that integrating e^(-ax^2) from 0 to +infinity has the solution of (pi/4a)^(1/2). So I just split the integral from -infinity to 0 and from 0 to +infinity (I get (pi/16)^(1/2) for the integral from 0 to +infinity). I am not sure how to evaluate the -infinity to 0 portion. Is there a better way to solve it?