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e^(i*2*pi) * (-1)^98 * (343)^(1/3)

Guest Jun 8, 2017

Best Answer 

 #1
avatar+2117 
+1

I will assume for this problem that i is for the imaginary number. If I should assume otherwise, tell me. I will, of course, simplify the given expression:
 

 

 

\(e^{i*2*\pi}*(-1)^{98}*343^{\frac{1}{3}}\) We will use an imaginary number rule here stating that \(e^{ia\pi}=(-1)^a, \text{so}\hspace{1mm}e^{i2\pi}=(-1)^2=1\). Of course, something multiplied by 1 is itself, so we are left with the other part.
\((-1)^{98}*343^{\frac{1}{3}}\) -1 raised to an even power is always one, so this is another part of the multiplication that we can eliminate.
\(343^{\frac{1}{3}}\) \(a^{\frac{1}{3}}=\sqrt[3]{a}\),so let's apply this rule, too.
\(\sqrt[3]{343}=7\) 7 is your answer.
   
   
   
   
   
   
TheXSquaredFactor  Jun 9, 2017
 #1
avatar+2117 
+1
Best Answer

I will assume for this problem that i is for the imaginary number. If I should assume otherwise, tell me. I will, of course, simplify the given expression:
 

 

 

\(e^{i*2*\pi}*(-1)^{98}*343^{\frac{1}{3}}\) We will use an imaginary number rule here stating that \(e^{ia\pi}=(-1)^a, \text{so}\hspace{1mm}e^{i2\pi}=(-1)^2=1\). Of course, something multiplied by 1 is itself, so we are left with the other part.
\((-1)^{98}*343^{\frac{1}{3}}\) -1 raised to an even power is always one, so this is another part of the multiplication that we can eliminate.
\(343^{\frac{1}{3}}\) \(a^{\frac{1}{3}}=\sqrt[3]{a}\),so let's apply this rule, too.
\(\sqrt[3]{343}=7\) 7 is your answer.
   
   
   
   
   
   
TheXSquaredFactor  Jun 9, 2017

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