Real and complex numbers: understanding the difference

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 discriminant is greater than zero, equal to zero, and less than zero:

Discriminant in the quadratic equation

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

Read also:

Solving a Quadratic Equation: Simple Steps