b. read none of magazine at all c. read exactly one of the magazines. 3. Use Mathematical induction to prove that $$ x^{n}+y^{n} $$ is divisible by $$ x+y $$ for odd natural number $$ n \geq 1 $$. 4. Solve the equation $$ z^{6}+1=\sqrt{3} i $$ where $$ z \in c $$.

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Bates Delgado · Accepted Answer

For part 3, the proof shows that $$ x^n + y^n $$ is divisible by $$ x + y $$ for all odd natural numbers $$ n \geq 1 $$. For part 4, the solutions to the equation $$ z^6 + 1 = \sqrt{3} i $$ are $$ z_k = \sqrt[6]{2} 	ext{cis}\left(\frac{\pi}{9} + \frac{k\pi}{3}ight) $$ for $$ k = 0, 1, 2, 3, 4, 5 $$.

b. read none of magazine at all c. read exactly one of the magazines. 3. Use Mathematical induction to prove that \( x^{n}+y^{n} \) is divisible by \( x+y \) for odd natural number \( n \geq 1 \). 4. Solve the equation \( z^{6}+1=\sqrt{3} i \) where \( z \in c \).

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b. read none of magazine at all c. read exactly one of the magazines. 3. Use Mathematical induction to prove that \( x^{n}+y^{n} \) is divisible by \( x+y \) for odd natural number \( n \geq 1 \). 4. Solve the equation \( z^{6}+1=\sqrt{3} i \) where \( z \in c \).

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