Final answer:
Mathematicians use the lowercase letter 'i' to represent the square root of -1. This imaginary unit is essential in complex numbers and is used when the discriminant in the quadratic formula is negative. The correct option is 4) i.
Step-by-step explanation:
The question asks which lowercase letter mathematicians use to express the square root of -1. In mathematics, especially in the field of complex numbers, the lowercase letter i is used to denote the square root of -1. This imaginary unit, i, is fundamental to complex numbers, which are numbers in the form of a + bi, where a and b are real numbers.
When dealing with quadratic equations or functions, we often encounter situations where we need to calculate the square root of a negative number. For example, the quadratic formula is used to find the values of x that satisfy the quadratic equation ax^2 + bx + c = 0. The discriminant, which is the part of the quadratic formula under the square root sign (√(b^2 - 4ac)), may sometimes be negative. When this is the case, we use the imaginary unit i to represent the square roots of negative numbers.
Therefore, the correct option to express the square root of -1 is 4) i.