Recent content by noahsdev

That makes sense. Thanks.

I've been messing around with numbers (as you do) and I'm wondering why this occurs.. lets let a = b-c. √a = √(b-c) =√(-(c-b)) =i√(c-b) =i√(-(b-c)) =i2√(b-c) =-√(b-c) =-√a For example if you let a = 1, b = 2, and c = 1.

I apologize if I am mistaken but I am doing advanced high school calculus and we are supposed to prove it using calculus and by treating i as a constant. Integrating complex functions is not part of the curriculum in any way but these are the instructions I have been given.

Finding the second derivative gives the same problem with the modulus. I also can't really use the value of θ as proof (for the first or second derivative), as I subbed it into find the value of c from the integral. Edit: would simply stating +-e^{i\theta} = cos(\theta)+ isin(\theta)...

I'm afraid I have to use straight calculus to solve.

Homework Statement Prove ei\theta = cos(θ) + isin(θ) Homework Equations The Attempt at a Solution Let g = cos(θ) + isin(θ) \frac{dg}{dθ} = -sin(θ) + icos(θ) => \frac{dg}{dθ} = ig => \frac{dθ}{dg} = \frac{1}{ig} => \frac{dθ}{dg} = -i\times\int\frac{1}{g} => θ = -i\timesln|g| + c => iθ - ic =...

I know how to factorize a polynomial over C, but what do complex factors show? Real factors show where the graph cuts the x-axis. I know how to do the calculations and pass the tests, but they never actually explain these type of things in textbooks. For example: z3-8z2+25z-26 =...

So how do I solve it? I mean, are you saying the rate of change is dT/dt = aT?

Homework Statement The number of termites in a colony is increasing at a rate proportional to the number present on any day. If the number of termites increases by 25% in 100 days, how much longer (to the nearest day) will it be until the population is double the initial number? 2. The attempt...

Thanks for the fast reply, my teacher wanted full working with identities so that's why it's in long form. I am not sure if it is a mistake or if it is a trick question, thanks.

Homework Statement Prove cot(x) - tan(x) = 2tan(2x) Homework Equations Trig identities http://en.wikipedia.org/wiki/List_of_trigonometric_identities The Attempt at a Solution I have worked it down and don't think they are equal. I think it's supposed to be 2cot(2x) not 2tan(2x)...

Homework Statement Consider the function ƒ:-k,k→R, where ƒ(x) = 1/√(k2-x2), where k is a positive constant. (i) Sketch the graph of y = ƒ(x) (ii) What is the domain of the function? Homework Equations ƒ(x) = 1/√(k2-x2) The Attempt at a Solution I don't understand how I am supposed...

Homework Statement Let f(z) = z3-8 and g(z) = f(z-1). This information applies to questions 1-5. 1. Express g(z) in the form g(z) = z3+az2 +bz + c 2. Hence, solve g(z) = 0. Plot solutions on an Argand diagram. Homework Equations Factorisation i2=-1 The Attempt at a Solution I have done...

Yes that makes sense. Thanks. P.S I know the quadrants haha I misstyped :)

OK, I have found the angle using x and y (cos and sin) and they both confirm that the calculator is correct. And yes, it does make sense since the complex number lies in quadrant 1 but why is the tan function wrong? I'm guessing you were hinting at that part but I really don't know. :)