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## History of Imaginary Numbers

Imaginary numbers were first developed by a Greek mathematician named **Hero of Alexandria**. The formulas for multiplying fictitious numbers were created later in **1572 **by the Italian mathematician **Gerolamo Cardano**. The square roots of negative numbers can be calculated using these numbers.

Let’s discover more about imaginary numbers, including their meaning, examples, and graphical explanations.

## What are Imaginary Numbers?

Imaginary numbers are those that, when squared, produce a negative number. They can also be thought of as the square root of negative numbers. An imaginary number is created by multiplying a non-zero real integer by the imaginary unit **“i”** (sometimes referred to as “iota”), where **i = √(-1) or i² = -1.**

Try squaring some real numbers now:

- (−3)² = −3×−3 = 9

- 4²= 4×4 = 16

- (1.3)² = 1.3×1.3 = 1.69

**Do any of the outcomes have a negative value?**

No. In other words, any real number’s square is always positive.

**What integer, then, yields a square that is negative?**

It is a fictitious quantity. When using the quadratic formula to solve quadratic equations, we frequently encounter the square root of negative numbers in math. Using imaginary numbers in these situations is required.

### Examples of imaginary numbers are shown below:

- √(-9) = √(-1) · √9 = i (3) = 3i
- √(-5) = √(-1) · √5 = i √5

**3i** and **i √5** are imaginary numbers in the examples above. Each of these numbers, as can be seen, is the result of multiplying a non-zero real number by **i**. We can therefore arrive at the following rule for imaginary numbers:**√(-x) = i √x**

These are a subset of complex numbers, which are created by adding together a real number and an imaginary number. In other words, a complex number has the formula **a + ib**, where **a **and **b** are both real numbers and a** bi **is an imaginary number.

### Graphical Representation of Imaginary Numbers

### FAQ

**Q1. What is 2i equal to?**

**Ans.** As we know that i²=-1 so

(2i)²=2ix2i=4i²=4x-1=-4

2i=√-4

**Q2. Is 0 an imaginary number?**

**Ans.** Zero is considered to be both a real and imaginary number.

**Q3. Is √2 an imaginary number?**

**Ans.** No, **√2 is an irrational number. **

Assume that √2 is a rational number. Let’s write √2 = m/ n, where m and n are two integers. Let’s also suppose that this fraction is in the lowest terms, which means that m and n must share a component because the fraction cannot be further simplified.

√2 = m/ n

Let’s square all sides, then multiply both sides by n²:

2 = m²/ n²

2 × n² = m²

Given that m² is an even number (a multiple of 2) and that an odd number squared is always an odd number, m must likewise be an even number. Since m is an even number, we can write m = 2x a for any other integer a.

2 × n² = (2 × a)²

2 × n² = 4 × a²

n² = 2 × a²

And now that we’ve established that m is even, we can conclude that n is also even by applying the same logic.

Since m and n are both even, the fraction m/n can be simplified by dividing the numerator and denominator by 2. M/N is therefore not in the lowest terms. Remember that we stated at the beginning that the fraction m/n is in the lowest terms; hence, we have a contradiction.

This proves that our earlier assumption that √2 is rational was incorrect. √2 is an irrational number.

If you want to know about Integers, then please check this article – 3 Types of Integers, Their Easy Explanations and Definition.