What's the square root of -1?

Question

How do negative numbers get broken down? We are told in school that you can't take the square root of negative numbers, but in reality it is possible.

Answer 1

The square root of -1 is represented by the letter i or j. Technically you can't take the square root of a negative number because you can't split the negative sign into two equal numbers. The letter i (and sometimes j) represent the square root of -1 which you can use to find the square root of the rest of the values inside the square root.

Example:

√(-4) = √(-1*4) = √(-1)*√(4) = i*2 = 2i

answer: 2i

Answer 2

The square root of -1 is represented by the imaginary unit, denoted as "i". It is defined as √(-1) = i. Imaginary numbers, such as i, are used in mathematics to represent quantities that cannot be expressed as real numbers. When it comes to negative numbers, they can be broken down using various mathematical operations, such as addition, subtraction, multiplication, and division, just like positive numbers. However, taking the square root of a negative number involves the use of imaginary numbers. Imaginary numbers come in the form of a+bi where "a" is real and "b" is imaginary, and they can be plotted on an imaginary axis.

I hope this helps!