Imaginary Numbers Are Real [Part 1: Introduction]

What is the function used in the example?

f(x) = x^2 + 1

What does the graph of f(x) = x^2 + 1 show?

It shows a parabola that does not cross the x-axis.

According to the Fundamental Theorem of Algebra, how many roots does a polynomial of degree n have?

It has exactly n roots.

What is the degree of the polynomial f(x) = x^2 + 1?

The degree is 2.

What problem arises when trying to find the roots of f(x) = x^2 + 1?

The function does not cross the x-axis, indicating no real solutions.

What historical figure proved that every polynomial equation has a specific number of roots?

Gauss.

What term describes the concept that every polynomial has n roots?

Fundamental Theorem of Algebra.

Where do the missing roots of the equation x^2 + 1 = 0 exist?

In a new dimension, represented by imaginary numbers.

What specific value do we need to find the roots of the equation x^2 + 1 = 0?

The square root of negative one.

What are imaginary numbers also referred to in this context?

Lateral numbers.

What counting system did early humans primarily use?

Natural numbers.

What significant mathematical innovation was developed by the Egyptians?

Fractions.

What do negative numbers help express?

Concepts like debt.

How did mathematicians of the past often deal with negative numbers in equations?

They would intentionally move terms around to avoid them.

What challenge does the equation x + 3 = 2 illustrate?

It showcases a situation where no solution exists without accepting negatives.

Luca Pacioli

Leonardo Da vinci’s math teacher who publish “Summa de Arithmetic” which was a comprehensive summary of all mathematics known in Renaissance Italy at the time.