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Given , and x2 = –1.

We need to prove (A + B)2 = A2 + B2.

Let us evaluate the LHS and the RHS one at a time.

To find the LHS, we will first calculate A + B.   We know (A + B)2 = (A + B)(A + B).     ( x2 = –1) To find the RHS, we will first calculate A2 and B2.

We know A2 = A × A.     ( x2 = –1)

Similarly, we also have B2 = B × B.    Now, the RHS is A2 + B2.   Thus, (A + B)2 = A2 + B2.

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