Imaginary numbers

[Beethequeen]

How do I simplify

i to the 17th power

i to the 22nd power

i to the 513th power


perhaps if possible can you list the steps also?
I'm trying to learn this!!

thank you!!

 

[pka]

How do I simplify

i to the 17th power

i to the 22nd power

i to the 513th power

Memorize this list: \(\displaystyle ~i^0=1,i^1=i,~i^2=-1,~i^3=-i,\).
Divide the power by 4. Find the remainder.

\(\displaystyle 17\div4\) has a remain \(\displaystyle 1\) so \(\displaystyle i^{17}=i^1=i\)

 

[Beethequeen]

Thank you So would i22= i2= -1 and i513=i1 = i ??

 

[Someone2841]

Thank you So would i22= i2= -1 and i513=i1 = i ??

Yes

 

[lookagain]

Thank you So would i22= i2= -1 and i513=i1 = i ??

Beethequeen,

you can show exponentiation with this symbol, "^."


Then your exercises/solutions would be

i^22 = i^2 = -1 and

i^513 = i^1 = i