# What happens when you Square an Imaginary Number?

The sum of a real number and an imaginary number is termed as a Complex number. These are the numbers that can be written in the form of a+ib. where a and b both are real numbers. It is denoted by z

The value of i is (√-1) or we can write as i^{2}= -1 .

**For example:**

- 3+4i is a complex number, where 3 is a real number (Re) and 4i is an imaginary number (Im).
- 2+5i is a complex number where 2 is a real number (Re) and 5i is an imaginary number (I’m)

The Combination of real number and imaginary number is called a Complex number .

**Imaginary Numbers**

The numbers which are not real are termed Imaginary numbers. After squaring an imaginary number, it gives a result in negative. Imaginary numbers are represented as Im().

Example: √-3, √-7, √-11 are all imaginary numbers. here ‘i’ is an imaginary number called “iota”.

**What happens when you square an imaginary number? **

The numbers which are not real are termed Imaginary numbers. **After squaring an imaginary number, it gives a result in negative**. Imaginary numbers are represented as Im(). A number that can be written as a real number multiplied by the imaginary unit i is termed as an imaginary number.

Example: √3i, √-4i, √-11 are all imaginary numbers. here ‘i’ is an imaginary number called “iota”. The value of i is (√-1) or we can write as i^{2 }= -1.

**Rules of imaginary numbers**

i = √-1

i^{2}= -1

i^{3}= -i

i^{4}= 1

i^{4n}= 1

i^{4n-1}= -1

### Sample Questions

**Question 1: If we** **square an imaginary number (4i)?**

**Solution: **

After squaring an imaginary number, it gives a result in negative …

(4i)

^{2}= 4i x 4i= 16i

^{2}= 16 (-1)

= -16

**Question 2: Find the square of (5i)?**

**Solution:**

After squaring an imaginary number, it gives a result in negative …

(5i)

^{2}= 5i x 5i= 25i

^{2}= 25(-1)

= -25

**Question 3: Find the square of (7i)?**

**Solution:**

After squaring an imaginary number, it gives a result in negative …

(7i)

^{2}= 7i x 7i= 49i

^{2}= 49(-1)

= -49

**Question 4: Find the square of 4i /25?**

**Solution:**

After squaring an imaginary number, it gives a result in negative …

{(4/25)i}

^{2}= 4i /25 x 4i /25= (4/25)

^{2}( i)^{2}= 16 / 625 (-1)

= -16/625

**Question 5: Find the square of -4i?**

**Solution:**

After squaring an imaginary number, it gives a result in negative …

(-4i)

^{2}= -4i x -4i= 16i

^{2}= 16(-1)

= – 16

**Question 6: Simplify (4 + 2i) – (3 + 4i), Find the square of imaginary number?**

**Solution:**

Given : (4 + 2i) – (3 + 4i)

= (4 – 3) + (2 – 4)i

= (1 – 2i)

Now imaginary number = -2i

(-2i)

^{2}= -2i x -2i= 4i

^{2}= 4(-1)

= – 4

**Question 7: Find the square of (10i)?**

**Solution:**

After squaring an imaginary number, it gives a result in negative …

(10i)

^{2}= 10i x 10i= 100i

^{2}= 100(-1)

= -100

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