Given:
The statement is
[tex](1+i)^2=2i[/tex]
To prove:
The given statement [tex](1+i)^2=2i[/tex].
Solution:
We have,
[tex](1+i)^2=2i[/tex]
Taking LHS, we get
[tex]LHS=(1+i)^2[/tex]
[tex]LHS=(1)^2+2(1)(i)+(i)^2[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex]LHS=1+2i+(-1)[/tex] [tex][\because i^2=-1][/tex]
On further simplification, we get
[tex]LHS=1+2i-1[/tex]
[tex]LHS=2i[/tex]
[tex]LHS=RHS[/tex]
Hence proved.
