Hello from Haknem School! Today we’re going to talk about two important types of numbers in mathematics: real and complex. These concepts may seem complicated, but don’t worry, we’ll break them down step by step.

## Real numbers

Real numbers are the numbers we use in everyday life. They include all natural numbers (1, 2, 3, …), integers (…, -2, -1, 0, 1, 2, …), rational numbers (numbers that can be expressed as a ratio of two integers, for example, 1/2, 2/3) and irrational numbers (numbers that cannot be expressed as a ratio of two integers, for example, the square root of two or the number Pi). Real numbers can be positive, negative, or equal to zero.

## Complex numbers

Complex numbers are numbers that include an “imaginary” unit, denoted as i. The imaginary unit is defined as the square root of -1. A complex number is usually written in the form a + bi, where a and b are real numbers, and i is the imaginary unit. Complex numbers are used in many areas of mathematics and physics, where they allow to solve equations that cannot be solved using only real numbers.

## In the context of quadratic equations

In the context of quadratic equations:

- if the
**discriminant is greater than zero**, the equation has**two real**roots. - If the
**discriminant is equal to zero**, the equation has**one real**root. - If the
**discriminant is less than zero**, the equation has no real roots, but has**two complex**roots.

Examples of solutions to quadratic equations in which the

discriminantisgreater than zero,equal to zero, andless than zero:

Now you know the difference between real and complex numbers and how they are used in mathematics. Keep learning and growing with Haknem School!

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