Square Root of -79

The square root is the inverse of the square of a number. Since -79 is a negative number, its square root is not a real number. In the complex number system, the square root of -79 is expressed in terms of the imaginary unit i, where i^2 = -1. Therefore, the square root of -79 is expressed as √(-79) = √79 * i.

The square root of a negative number involves the imaginary unit i, which is defined as √(-1). The square root of -79 can be calculated using this concept:

Step 1: Express -79 as a product of its positive counterpart and -1.

Step 2: Use the property √(a * b) = √a * √b.

Step 3: Express √(-79) as √79 * √(-1) = √79 * i.

To express the square root of -79 in complex form, we use the imaginary unit i:

Step 1: Recognize that -79 can be written as 79 * -1.

Step 2: Apply the property √a * √b = √(ab) to get √79 * √(-1).

Step 3: Replace √(-1) with i to obtain √79 * i.

Thus, the square root of -79 in complex form is √79 * i.

To compute the square root of -79 using a calculator that supports complex numbers, follow these steps:

Step 1: Input 79 into the calculator and find its square root, which is approximately 8.888.

Step 2: Recognize that the square root of -79 is the result multiplied by i (the imaginary unit).

Step 3: Display the result as 8.888i.

Negative square roots, involving the imaginary unit i, are used in advanced mathematics and engineering, particularly in fields dealing with complex numbers. Some applications include: - Electrical engineering, particularly in analyzing AC circuits. - Quantum mechanics, where complex numbers describe wave functions. - Control theory, used for system stability analysis.

• Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For negative numbers, this involves the imaginary unit.
   
• Imaginary unit: Denoted as i, it is defined by the property i^2 = -1. It is used to express square roots of negative numbers.
   
• Complex number: A number of the form a + bi, where a and b are real numbers, and i is the imaginary unit.
   
• Modulus: The modulus of a complex number a + bi is the distance from the origin to the point (a, b) in the complex plane, calculated as √(a^2 + b^2).
   
• Argument: The angle formed between the positive real axis and the line representing the complex number in the complex plane.