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Show that ( 1 +i )2 = 2i

Show that ( 1 +i )2 = 2i-example-1
User Jpbochi
by
6.2k points

1 Answer

5 votes

Given:

The statement is


(1+i)^2=2i

To prove:

The given statement
(1+i)^2=2i.

Solution:

We have,


(1+i)^2=2i

Taking LHS, we get


LHS=(1+i)^2


LHS=(1)^2+2(1)(i)+(i)^2
[\because (a+b)^2=a^2+2ab+b^2]


LHS=1+2i+(-1)
[\because i^2=-1]

On further simplification, we get


LHS=1+2i-1


LHS=2i


LHS=RHS

Hence proved.

User Ziv Levy
by
7.4k points
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