# Tagged Questions

1answer
26 views

### the absolute value of $\frac{1}{e^{i\omega t}-1}$

I am told to get the absolute value of $$\frac{1}{e^{i\omega t}-1}$$ I sense that there's something ridiculously simple about this, but I tried working from the fact that if I square it, the absolute ...
2answers
49 views

### Can I conjugate a complex number: $\sqrt{a+ib}$?

Can I find the conjugate of the complex number: $\sqrt{a+ib}$? Actually my maths school teacher says and argues with each and every student that we can't conjugate "square root of $a+ib$" to "square ...
0answers
33 views

### Weird conformal map problem

Construct a conformal map from the region $\omega$ = open disk of radius 1 centered at 0 minus the closed disk of radius 0.5 centered at 0.5 to $\mathbb{D}$ = disk radius 1 centered at 0. I really ...
1answer
44 views

### Let $f(z) = z + z^2$ and let $V = \displaystyle \{z \in \mathbb{C} : |z| < \frac{1}{2}, \frac{3\pi}{4} < arg\{z\} < \frac{5\pi}{4}\}$.

Let $f(z) = z + z^2$ and let $V = \displaystyle \{z \in \mathbb{C} : |z| < \frac{1}{2}, \frac{3\pi}{4} < arg\{z\} < \frac{5\pi}{4}\}$. $(a)$ Show that $f(V) \subset V.$ $(b)$ Let $f_n$ be ...
4answers
52 views

### Writing the complex number $z = 1 - \sin{\alpha} + i\cos{\alpha}$ in trigonometric form

Now I can't finish this problem: Express the complex number $z = 1 - \sin{\alpha} + i\cos{\alpha}$ in trigonometric form, where $0 < \alpha < \frac{\pi}{2}$. So the goal is to determine both ...
2answers
33 views

### rationalize the complex number multiplication rule

For a middle school student without previous knowledge of complex number, how do one introduce the multiplication rules of complex number? i.e., if we have two real number pairs of $(a,b)$ and ...
1answer
46 views

### Factoring a complex polynomial

Factorize the polynomial : $$p(x) = x^{5} - x^{4}+ 4x - 4$$ In real factors in the lowest degree possible. So in previous questions I have been given at least one rot so that I can factorize it ...
3answers
66 views

### Complex Equations

The Equation: $$z^{4} -2 z^{3} + 12z^{2} -14z + 35 = 0$$ has a root with a real part 1, solve the equation. When it says a real part of 1, does this mean that we could use (z-1) and use ...
1answer
75 views

2answers
76 views

### Complex Numbers - Finding Roots

Hi there I was wondering if someone could help me? I am struggling to find the roots of the polynomial $z^4+2z+3=0$ It is not a quadratic so can't use the quadratic formula so am not quite sure ...
4answers
49 views

### want to prove exponential identity with complex numbers

I want to prove that $e^{x+y}=e^x*e^y$, where x and y are complex numbers. I only want to use that evey complex number is on the form $z=a+bi$, where $i^2=-1$. And if z is a complex number we have ...
2answers
41 views

### Construction of complex numbers and exponent rules for them

I have some questions about the construction of the complex numbers in this Wikipedia article, especially of the exponents of complex numbers. $1$. Is it enough to define it as $a+bi$, where a,b are ...
2answers
36 views

### Separating a Complex Valued Function

Is there a formula (with mathematical reasoning) for separating a complex-valued function $f(z)=f(x+iy)$ into the form $f(z)=u(x,y) + iv(x,y)$? Thank You, C.A
2answers
74 views