Alg6.1.5

From Exampleproblems

Solve $(1+i)^{4}\,$

Expressing the expression in the following way, $((1+i)^{2})^{2}\,$

$(1+i^{2}+2(1)(i)+i^{2})^{2}\,$

$(1+i^{2}+2i)^{2}\,$

Substituting the value of $i 2 = - 1$ in the expression

$(1-1+2i)^{2}\,$

$(2i)^{2}\,$

$(2^2)(i^{2})\,$

$4(-1)\,$

The solution is $-4\,$