Mathematics

Problem

60. Group Activity The Square Roots of

i

Let

a

and

b

be real numbers such that

(a+b i)^{2}=i

. (a) Expand the left-hand side of the given equation. (b) Think of the right-hand side of the equation as

0+1 i

, and separate the real and imaginary parts of the equation to obtain two equations. (c) Solve for

a

and

b

. (d) Check your answer by substituting them in the original equation. (e) What are the two square roots of

i