Algebra 2 - Why do we use complex numbers for square roots

The video tutorial covers the concept of square roots, explaining that the square root of a number is the reciprocal of squaring. It discusses irrational numbers, like sqrt(5), which cannot be expressed as a simple fraction. The tutorial then introduces imaginary numbers, explaining that the square root of a negative number is not possible in the real number system. To address this, the imaginary number system is introduced, where sqrt(-1) is defined as 'i'. The video further explains how to work with imaginary numbers, using examples like sqrt(-16), and demonstrates how to express such numbers using the imaginary unit 'i'.

What is the imaginary number system and why is it important?

How can we express the square root of -16 using the imaginary number system?