SOLUTION: Find the power of the following complex number: z=(sqrt(2)-i)^(4) This one has been killing me.... thanks

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Question 374909: Find the power of the following complex number: z=(sqrt(2)-i)^(4)
This one has been killing me.... thanks
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let z=x%2Biy
Then,
z%5E4=%28x%5E4-6x%5E2y%5E2%2By%5E4%29%2Bi%284x%5E3y-4xy%5E3%29
In this case,
x=sqrt%282%29
y=-1

z%5E4=%284-12%2B1%29%2Bi%28-8%2Asqrt%282%29%2B4%2Asqrt%282%29%29
z%5E4=%28-7%29%2Bi%28-4%2Asqrt%282%29%29
highlight%28z%5E4=%28-7%29-%284%2Asqrt%282%29%29%29i

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


First remember the properties of exponents:



So, rewrite your problem:



Next, remember the pattern for squaring a binomial:



And don't forget that

So



And so far we have:



Now repeat the process:



John

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