anonymous
  • anonymous
simplify i^6 times i^8
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
(i^6)(i^8) =i^14 =-1
anonymous
  • anonymous
but, is i a variable or complex number?
anonymous
  • anonymous
if its a variable, leave it as i^14

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Akshay_Budhkar
  • Akshay_Budhkar
\[i^{6+8}=i^{14}=i^{4n+2}=-1\]
anonymous
  • anonymous
where did the i go? and where did the 4n+2 come from?
Akshay_Budhkar
  • Akshay_Budhkar
14= 4 (3) +2 which is of the form 4n +2
Akshay_Budhkar
  • Akshay_Budhkar
is "i" complex number?
anonymous
  • anonymous
wait, ofree, answer the question
anonymous
  • anonymous
Is i a complex number?
Akshay_Budhkar
  • Akshay_Budhkar
or is it a variable?
Akshay_Budhkar
  • Akshay_Budhkar
\[x^a \times x^b= x^{a+b}\] Remember that.. i believe it is a variable
Akshay_Budhkar
  • Akshay_Budhkar
so your answer is \[i^{14}\]
anonymous
  • anonymous
What Akshay is doing is showing you how to figure out the system of complex numbers. the root of -1 is called i. Therefore, i^2=-1 and i^4 is 1. 4n+2 refers to this pattern for complex numbers.
anonymous
  • anonymous
the only options are i, -1, -i, 1 so i^14 is not the answer

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