a a

Using the definition of the derivative find at which points the function f(z) = Im(z)/zconjugate is complex differentiable. I know that it is not complex differentiable anywhere but I need to show it using the definition and not the Cauchy Riemann equations

Find the solutions to the equation the conjugate of z equals z^3 where z is a complex number. Please give a step by step solution. Thank you.

Solve (1 - (sqrt(3) - i) / 2) ^ 24. Please provide a step by step solution. Thank you.

let x,y be irrational and r be rational

so i know that an irrational times a rational is irrational since if it was rational then x * r = m / n

=> x = m / (n * r) E Q and is therefore a contradiction

from this why can it not be proven that an irrational divided by or multiplied by an irrational is irrational ( I know that this is false)

since x * r = y => x = y/r => x/y = 1/r => y/x = r E Q

and then y * 1/x = r and since the inverse of an irrational is irrational (if not x^-1 = m/n => x =n/m )

y * an irrational = r

I know this is false since I know of counterexamples, but where does this proof fail?

So I am trying to answer a question that asks to count the nodes in a binary tree and print this information in the function. If this is done recursively: if (tree != NULL) { call with left child, count, call with right child }, and then it is printed before returning, wouldn't the count print multiple times before each return and each time with a different count?

Is there any way to do this recursively inside the function so it only prints once at the final count?

A box contains 5 green and 10 red balls. 8 balls are drawn, with replacement after each draw. What is the probability that you get a green ball 2 times and a red ball 6 times?

I know the equations to do probability problems but I am trying to develop a more intuitive sense of how to do the problems. So I am trying to figure out the probability of two pair and right now what I have is the first card is 52/52 the second would be 3/51 the third 48/50 fourth 3/49 and fifth 44/48. These cards can be ordered 5! ways but need to be divided by 2! * 2! as there are two pairs of the same card. The answer I get is two times the correct answer so it seems that I need to divide the numerator by an additional 2, but I don't know how to explain it. Where does the two come from?

(Additionally, do you know of any sources that demonstrate probability in this way rather than just using the equations?)

When you are doing compositions of linear transformations and you are given first one function to perform and then a second one (ex: rotate counterclockwise 90 degrees and then reflect in the line y=x) and you are trying to find the matrix that will do both simultaneously i know that you need to multiply the two matrices, but in what order do you multiply them (in a x b which matrix is a and which is b)?

Regarding this triangle: http://www.csgnetwork.com/righttricalc.html

How would you use the right hand rule on AB X CB (both pointing toward B)?

Would the cross product vector be pointing toward you?

I am uncertain exactly when some vectors span the entire space. What I think I know at this point is that in a given space r^n, a set of vectors that are equal to that number n will span that entire space as long as any of those vectors are not multiples of each other, combinations of the other vectors and are not the zero vector. If the number of vectors is less than n, I am pretty sure that it will not span the space. However, I can not think of a clearly demonstrable proof for this (when it does not span the space), although it does seem to make sense intuitively when I think about it geometrically.

How did the development of an Atlantic world impact the kingdom and colonies that were part of it? 3 examples

Use series to approximate the definite integral: (1 + x^4)^1/2 with the limits of 0 and .4 . I know you are supposed to use the known geometric series of 1/1-x, but i am unsure of how to manipulate this integral to be put into a similar form.

So I need a bit of help in economics. Here is the question:

Keynesian theory says that gov't can do 3 things to move out of recession: reduce interest rate, reduce taxes and increase gov't spending. For each approach discuss its strengths as a policy tool and its weaknesses as a policy tool.

find the point closest to (0,8) on the curve x2 - y2 = 16 (the 2s mean squared).

how would gold function as a medium of exchange, store of value and unit of account in relation to US money?

After reading Hume do away with inductive reasoning, I wondered how is it then that we can know anything deductively either? Any argument to show that a priori knowledge is true (ie through the principle of non-contradiction) further requires a priori reasoning and deductive argumentation, which would assume those methods are in fact true and thereby makes it circular.

when you have something like the square root of csc^2 (x^2 + 4), does the fact that it is csc squared cancel out the square root or do you have to take the square root of (csc (x^2 + 4))^2?

(a) Show that of all the rectangles with a given area, the one

with smallest perimeter is a square.

(b) Show that of all the rectangles with a given perimeter, the

one with greatest area is a square.