The value of i, known as the imaginary unit, is defined as the square root of -1. In mathematical terms, this means:
- i = √(-1)
- i2 = -1
This unit is fundamental in the field of complex numbers. A complex number is expressed in the form of a + bi, where a is the real part and bi is the imaginary part of the complex number.
To calculate any power of i, it helps to remember its cyclic nature:
- i1 = i
- i2 = -1
- i3 = –i
- i4 = 1
Therefore, for any integer exponent, you can find i’s value by reducing the exponent modulo 4. This unique property illustrates how i plays a crucial role in advanced mathematics, especially in solving quadratic equations and in engineering fields.