please help me...

1. When squaring a complex number using De Moivre's theorem, there are two answers.

TRUE
FALSE

i think it's true, but I'm not sure.

thanks.

false. r^2 and 2θ only have a single value each.

thank you

You are correct. When squaring a complex number using De Moivre's theorem, there are indeed two answers. The two answers are conjugates of each other and correspond to the two possible square roots of the complex number.

To determine whether the statement "When squaring a complex number using De Moivre's theorem, there are two answers" is true or false, we need to understand De Moivre's theorem and how it applies to squaring complex numbers.

De Moivre's theorem states that for any complex number in the form z = r(cosθ + isinθ), where r is the modulus (or magnitude) of the complex number and θ is the argument (or angle) of the complex number, the n-th power of z is given by z^n = r^n(cos(nθ) + isin(nθ)).

In this case, we are looking specifically at squaring a complex number, which means n = 2. So, if z = r(cosθ + isinθ), then z^2 = r^2(cos(2θ) + isin(2θ)) according to De Moivre's theorem.

From this expression, we can see that squaring a complex number using De Moivre's theorem results in an answer in the form z^2 = r^2(cos(2θ) + isin(2θ)). Here, there is only one answer specified by the given expression.

Therefore, the statement "When squaring a complex number using De Moivre's theorem, there are two answers" is FALSE. There is only one answer when squaring a complex number using De Moivre's theorem.