Math Is Fun Forum

Can't do it.

I hope you'll put some sort of "real-time" mechanism to tell us if the number we put into the sudoku box is wrong (maybe the box will turn red or something). It helps a lot to figure out our mistakes, rather than waiting till the end, and suddenly realising that there's a mistake.

Hi, Kimrei, does SA mean South Australia or somewhere else?

I didn't know you had to put them in [math] tags.

You got the numerator in your answer wrong for 5 and 6, that's according to Scientific Workplace.

Btw, how do you enter the equations directly in here? I tried using the Latex syntax to do it but it wouldn't display properly.

It's not that, but this has a little story behind it.

A biotech major has to take stats (originally). With chem, he has to do a slightly harder unit called Applied Maths (which of course involves DEs).

Now with me, I saw what the Applied Maths syllabus was and I was shocked. Most of it, I've covered in college! So, I applied for a preclusion (which shouldn't have been granted because later I found out, whatever you did in college didn't count in uni. Turns out I was lucky.)

Also, no one in the world (I think) would do such a degree as I'm doing (Biotech, Chem, maths minor) in 3 years because I think it is really stressful.

And yes, Bio major needs to know DE now, we use a lot of it in modelling. With partial derivatives too I think.

Complex numbers addition and subtraction, think about this as normal algebra. Eg: a+a=2a, a+b=a+b.
For your example: Z1+Z2=2+4i+6-3i=(2+6)+(4-3)i=8+i

For multiplication, just do it as normal algebra, except, remember that i^2=-1. So anywhere you have an i^2, replace with -1, and you're on your way.

Division would be the hardest of all. Have you learnt about conjugates? Take the conjugate of Z2, i.e., 6+3i and set up your equation like in the picture. Now do the same thing as with multiplication, treat it as if it is algebra, only remember to replace i^2=-1.

For Argand diagrams, first find the product of the equation eg, for Z1+Z2+Z3, you would have found the answer in (b). Plot the x and y coordinates, put the real part on the x coordinate and imaginary part on the y coordinate. Eg, for 3+4i (it's not the answer), I would plot the point (3,4). Then connect a line from the origin (0,0) to the point you've plotted, put an arrow in its direction, and you have your answer.

That's the second problem done using integration by parts, it wasn't too bad (Add the constant at the end if you want). Trust me, you wouldn't want to use integration by parts for the first problem, it can get very messy.

I don't really know how to use the "power rule" for the first problem.

Does it specifically state integration by parts? I think using partial fractions might be easier.