Mister Exam
|1/z-i|>=1 inequation
The solution
You have entered
[src]
|1 | |- - I| >= 1 |z |
$$\left|{- i + \frac{1}{z}}\right| \geq 1$$
|-i + 1/z| >= 1
Detail solution
Given the inequality:
$$\left|{- i + \frac{1}{z}}\right| \geq 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{- i + \frac{1}{z}}\right| = 1$$
Solve:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$\left|{- i + \frac{1}{z}}\right| \geq 1$$
so the inequality has no solutions
$$\left|{- i + \frac{1}{z}}\right| \geq 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{- i + \frac{1}{z}}\right| = 1$$
Solve:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
x0 = 0
$$\left|{- i + \frac{1}{z}}\right| \geq 1$$
| 1| |I - -| >= 1 | z|
so the inequality has no solutions
Rapid solution 2
[src]
(-oo, 0) U (0, oo)
$$x\ in\ \left(-\infty, 0\right) \cup \left(0, \infty\right)$$
x in Union(Interval.open(-oo, 0), Interval.open(0, oo))
Rapid solution
[src]
And(x > -oo, x < oo, x != 0)
$$x > -\infty \wedge x < \infty \wedge x \neq 0$$
(x > -oo)∧(x < oo)∧(Ne(x, 0))