Calculus I, II and III

Complex Analysis

The square root of a number is a value that, when multiplied by itself, gives the original number. For positive real numbers, the square root has two solutions: a positive and a negative value. However, when we consider the square root of a negative number, we enter the realm of complex numbers. The square root of negative one is denoted as $\sqrt{-1}$. In the field of complex numbers, the square root of negative one is represented by the imaginary unit, which is symbolized by the letter $i$. The imaginary unit $i$ is defined by the property that $i^2 = -1$. Therefore, the square root of negative one is: $$\sqrt{-1} = i$$ This concept is fundamental in complex number theory and is widely used in various fields of science and engineering, including electrical engineering, quantum physics, and signal processing, where complex numbers provide a powerful mathematical tool for solving problems involving two-dimensional quantities.

Question

What is the square root of negative 1?

Solution

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