Radicals and Complex Numbers

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). It represents the operation of finding a number that, when multiplied by itself a certain number of times, gives the original number.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

The imaginary unit 'i' is defined as $$i = \frac{\text{√-1}}{1}$$ . It is used to represent the square root of negative numbers.

The principal square root of a number x is the non-negative value that, when squared, gives x. It is denoted as $$\text{√}x$$ .

$$\text{√}a^2 = |a|$$ , where |a| is the absolute value of a.

$$\text{√}xy = \text{√}x \times \text{√}y$$ , provided x and y are non-negative.

$$\text{√}a/b = \frac{\text{√}a}{\text{√}b}$$ , provided b is not zero.

The sum is -2 + 6i.

$$\text{√}125 = 5\text{√}5$$ .