Square Root of a Negative Number
Square Root of a Negative Number
Negative numbers have no real square root. This is because any real number multiplied by itself is always positive or zero — never negative.
The imaginary unit i
i = √−1 therefore i² = −1
Mathematicians invented the imaginary unit i to represent √−1. Using i, we can express the square root of any negative number.
Formula
√(−a) = i√a (where a > 0)
Examples
- √−1 = i
- √−4 = i√4 = 2i
- √−9 = i√9 = 3i
- √−25 = i√25 = 5i
- √−2 = i√2 ≈ 1.4142i
Complex numbers (like 3 + 4i) combine real and imaginary parts and are used widely in engineering, physics, and signal processing.