# Tagged Questions

Questions involving complex numbers, that is numbers of the form $a+bi$ where $i^2=-1$ and $a,b\in\mathbb{R}$.

32 views

### complex variables problem [closed]

By using the polar form of the complex number prove that, $|z_1 z_2| = |z_1| |z_2|$ and $\left|\frac{z_1}{z_2}\right| = \frac{|z_1|}{|z_2|}$
35 views

### Re-defining the complex unit for teaching purposes

I often come across students who are confused by the idea that the complex unit, $i$, is defined as $i^2 = -1$. Since we are using the complex numbers in an engineering course, we use the complex ...
52 views

### Is this matrix going to be real or complex?

I hope that this is the right forum where to post this question (and not here). I have a Chi-Square Kernel Matrix (using the second version, which is positive-definite) ...
38 views

### Find modulus of $\frac{|z_1-z_2|}{|1-(z_1)(\overline{z_2})|}$ [closed]

If $z_1$ and $z_2$ are two different complex numbers and $\lvert z_1\rvert=1$ then find $$\frac{\lvert z_1-z_2 \rvert}{\lvert 1-z_1\bar{z_2} \rvert}$$
45 views

51 views

### Find |z| if the given expression is purely imaginary [closed]

Find $|z|$ if $\dfrac{z-2}{z+2}$ is entirely imaginary. I know that if a number is purely imaginary, then $z-\overline{z}=2i$(some integer)
40 views

### Find the modulus of $|z-5|/|1-3z|$ when z is given

If $z = 3-2i$ then find $$\frac { \left| z-5 \right| }{ \left| 1-3z \right| }$$ I've substituted z by $|z|^2/z$ conjugate but still cant figure out what to do, Thanks in advance
54 views

### Roots of Unity with Rational Real Parts

All of the $4^{\text{th}}$ and $6^{\text{th}}$ roots of unity have real parts that are rational numbers. Are these the only roots of unity $z$ such that $\text{Re}(z)\in \mathbb{Q}$ ?