Unreal Numbers

Unreal number is also called as imaginary number. An unreal number is a number in the form yi where y is a non-zero, real number and i, defined by i2 = − 1, is known as the imaginary unit. An imaginary number or unreal number yi can be added to a real number x to form a complex number of the form x+ yi, where x and y are called respectively, the "real part" and the "imaginary or unreal part" of the complex number x + yi.

Example problems of unreal numbers:

Unreal numbers example 1:

Simplify 7i + 6i

Solution:

We can find the addition value of given imaginary number.

Given problem is 7i + 6i.

Here both 7i and 6i are the imaginary number.

In the above problem, we can take i for common. Then we get,

7i + 6i= i (7+6)

Add the values for inside the parenthesis.

7+6=13

Therefore, i(13)= 13i

Answer: 13i

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Unreal numbers example 2:

Simplify (2i+ 5i) 2

Solution:

We can find the square value of given unreal numbers.

Given problem is (2i+ 5i) 2

Here both 2i and 5i are the imaginary numbers.

Now we can square the above problem.

i* i= i2

i2=-1

That is, ((2i+ 5i) 2= (7i) 2

=49(i) 2

Here substitute the value of i2 into the above.

Then we get,

49i2=49(-1)

=-49

Answer: -49

Unreal numbers example 3:

Simplify 5i- 8i

Solution:

We can find the subtraction value of given imaginary number.

Given problem 5i- 8i

Here both 5i and 8i are the imaginary numbers.

In the above problem, we can take i for common. Then we get,

5i- 8i = i (5-8)

Subtract the values for inside the parenthesis.

5-8= -3

That is, i (-3)

= -3i

Answer: -3i

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Practice problems of unreal numbers:

1. Simplify (8i) 2              Answer: -64

2. Simplify i+ 7i          Answer: 8i

3. Simplify 12i-9i        Answer: 3i