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What happens when you Square an Imaginary Number?

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  • Last Updated : 08 Mar, 2022

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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