Question

Simplify and Solve

4 square root of -13 - 6 square root of -13

Answer 1

Conditions

Simplify and Solve

4 square root of -13 - 6 square root of -13

Solution

$$4 \sqrt{-13} - 6 \sqrt{-13}$$

This is the task for using operations with the complex numbers.

As we know, the definition claims, that:

$$\sqrt{-1} = i$$

Then

$$\sqrt{-13} = \sqrt{(-1) \cdot 13} = i \sqrt{13}$$ $$4 \sqrt{-13} - 6 \sqrt{-13} = 4i\sqrt{13} - 6i\sqrt{13} = -2i\sqrt{13}$$

Answer: $2i\sqrt{13}$