QuestionSolve the compound inequality: $i \cdot x \leq 3$ .

Studdy Solution

STEP 1

Assumptions1. The inequality is given as $ix \leq3$ . i is the imaginary unit, which is defined as $i = \sqrt{-1}$

STEP 2

To solve the inequality, we first need to isolate x. We can do this by dividing both sides of the inequality by i.
$x \leq \frac{}{i}$

STEP 3

Now, we need to simplify the right side of the inequality. To do this, we multiply the numerator and the denominator by the conjugate of i, which is -i.
$x \leq \frac{3(-i)}{i(-i)}$

STEP 4

implify the denominator.
$x \leq \frac{3(-i)}{-1}$

STEP 5

implify the right side of the inequality.
$x \leq -3i$ This is the solution to the compound inequality. However, it's important to note that inequalities with complex numbers are not well-defined in the same way they are for real numbers. The solution $x \leq -3i$ doesn't have a clear meaning in the complex plane, as there's no inherent ordering of complex numbers like there is for real numbers.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms