Question

If (a+bi)^2=2abi, what must be the relationship between a and b? Show or explain your reasoning.

Answer 1

$(a+bi)^2 =(a+bi)(a+bi)= a^2 +2abi+b^2 i^2 \\ \\ i^2 = -1 \\ \\ (a+bi)^2 = a^2-b^2 +2abi = 2abi \\ \\ a^2 -b^2 = 0 \\ \\ a^2 = b^2 \\ \\ a = b$

For the statement to be true, 'a' and 'b' must be equal

*First expand the binomial using FOIL, then set it equal to whats given "2abi".
Then you can find the relationship between a and b.