Question

Every real number is a complex number. Proof

Answer 1

Answer:

So, a Complex Number has a real part and an imaginary part. But either part can be 0, so all Real Numbers and Imaginary Numbers are also Complex Numbers.

Answer 2

Given :   real number & complex number

To find : Show that Every real number is a complex number

Solution:

A complex number is a number that can be expressed in the form Z  = x + iy where x  and y are real numbers

x is a real number

hence x ∈ R

y is a real number

hence y ∈ R  

 Z  = x + iy  

as y ∈ R   => 0 ∈  y

taking value of y as 0

=> Z  = x  +  i(0)

=> Z  = x  

=> x  = Z     when y = 0

Hence  Every real number is a complex number with  imaginary part being zero

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