Complex Numbers Question (1 Viewer)

[turkey]

I was writing notes on the syllabus and as i was goin though power and roots of complext nubmers there was a dot point

*find any integer power of a given complex number...

and i was stumped cause i had never.. came across one of those questions.. prob cause i didn't do enough questions T0T so could anyone tell me how would i attempt one.. sayy

the question asked find the values of n for which (√3 + i)^n - (√3-i)^n = 0 where n is a positive integer..
it said to use demoivre's theorem.. but i didn' t know how to attempt it >__< i'm slight thick at these kinda things too T0T

 

[Elvin]

im pretty sure the answer is,

n is any integer except |n|<7 (its actaully 'n' less than OR EQUAL to 6 but theres no sign on my keyboard so yeah)

i just made it into mod arg form did de moivre simplified then eventaully got
2^n x 2 (isin npi/6)=0
then got rid of 2^n x 2 and got

npi/6=kpi where k is +or- 1, +or-2, +or-3...

the pi's cancel out and u get
n=6k
so from there i got my answer
n is n e integer cept -7 < n < 7

 

[turkey]

oh thankyou ^^