Square Root of -26

The square root is the inverse of squaring a number. While the square root of a positive number is a straightforward calculation in the realm of real numbers, the square root of a negative number involves imaginary numbers. The square root of -26 is expressed using the imaginary unit 'i', where i is defined as √-1. Therefore, the square root of -26 in terms of complex numbers is written as √-26 = √26 * i.

Complex numbers are used when dealing with the square roots of negative numbers. A complex number comprises a real part and an imaginary part. In the context of -26:

- The real part is 0.

- The imaginary part is √26 * i.

To find the square root of -26, we use the property of imaginary numbers:

Step 1: Recognize that the square root of a negative number involves 'i'.

Step 2: Express -26 as -1 * 26.

Step 3: Separate the square root into √-1 * √26.

Step 4: Replace √-1 with 'i', giving the result as √26 * i.

Let's explore how to work with the square root of -26 in practical scenarios: Example 1: If z = √-26, then |z|, the modulus of z, is √26.

Example 2: The square of z = √-26 is -26, demonstrating that (√-26)² = -26.

• Square root: The inverse operation to squaring a number. For negative numbers, it involves imaginary numbers.
   
• Imaginary number: A number that can be written as a real number multiplied by the imaginary unit 'i', where i² = -1.
   
• Complex number: A number that has both a real part and an imaginary part, expressed as a + bi.
   
• Modulus: The magnitude of a complex number, calculated as √(a² + b²) for a complex number a + bi.
   
• Exponential notation: A way of expressing numbers using powers, often used with complex numbers involving 'i'.