# 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 i2 = -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 i2 = -1.

Rules of imaginary numbers

i = √-1

i2 = -1

i3 = -i

i4 = 1

i4n = 1

i4n-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

= 16i2

= 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

= 25i2

= 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

= 49i2

= 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

=  16i2

=   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

=  4i2

=  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

=  100i2

=  100(-1)

= -100

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