Solution
... In the last statement, what happens if we remove the assumption that k ≥ 1? Solution: We needed k ≥ 1 to ensure that mnk−1 is an integer. For example, if k = 0, then nk−1 = 1/n. 8. Let b, c, x ∈ R. (a) Prove that x satisfies the equation x2 + bx + c = 0 if and only if x satisfies the equation (x + b ...
... In the last statement, what happens if we remove the assumption that k ≥ 1? Solution: We needed k ≥ 1 to ensure that mnk−1 is an integer. For example, if k = 0, then nk−1 = 1/n. 8. Let b, c, x ∈ R. (a) Prove that x satisfies the equation x2 + bx + c = 0 if and only if x satisfies the equation (x + b ...
THE COMPLEX EXPONENTIAL FUNCTION
... this. You can differentiate eibt by means of (3) and the chain rule. You will still have some algebra to do to get the form on the right of (9). 5. Find an identity for sin 3θ using n = 3 in De Moivre’s formula. Write your identity in a way that involves only sin θ and sin 3 θ if possible. ...
... this. You can differentiate eibt by means of (3) and the chain rule. You will still have some algebra to do to get the form on the right of (9). 5. Find an identity for sin 3θ using n = 3 in De Moivre’s formula. Write your identity in a way that involves only sin θ and sin 3 θ if possible. ...
