## anonymous 4 years ago simplify i^6 times i^8

1. anonymous

(i^6)(i^8) =i^14 =-1

2. anonymous

but, is i a variable or complex number?

3. anonymous

if its a variable, leave it as i^14

4. Akshay_Budhkar

$i^{6+8}=i^{14}=i^{4n+2}=-1$

5. anonymous

where did the i go? and where did the 4n+2 come from?

6. Akshay_Budhkar

14= 4 (3) +2 which is of the form 4n +2

7. Akshay_Budhkar

is "i" complex number?

8. anonymous

9. anonymous

Is i a complex number?

10. Akshay_Budhkar

or is it a variable?

11. Akshay_Budhkar

$x^a \times x^b= x^{a+b}$ Remember that.. i believe it is a variable

12. Akshay_Budhkar

so your answer is $i^{14}$

13. 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.

14. anonymous

the only options are i, -1, -i, 1 so i^14 is not the answer