Question

Expand (5-5i)^4
Could someone walk me through this?

Answer 1

U simply represent this like this from exonenets addition and subtraction rules : \[(5-5i)^2*(5-5i)^2\]
Each is then exanded to : \[(5^2 - 50i + 25 i^{2} )\] which is simply : 25 - 50i - 25 = -50i
then the original equation simplify to : -50i * -50i = \[250i^2 = -250\]

Answer 2

Let me know if you got it :)

Answer 3

I understand what you did but there is an answer key and it says the answer is \[2500(\cos \frac{ 28\Pi }{ 4 } + i \sin \frac{ 28\Pi }{ 4 }) =1.511-.450i\] how would i get to here

Answer 4

you can use
z=5-5i

work this out in the form
z=r(cosx+isinx)

then z^4 would be

z=r^4(cos4x+isin4x)

Answer 5

\[z^{4}=r^{4}(\cos4x+isin4x)\]

Answer 6

fixed it

Answer 7

hmm

Answer 8

So
r is the magnitude of your imaginary number

and x is the inverse tan of b/a
where b is the coefficient of imaginary number
and a is the real part

Answer 9

\[r=\sqrt{(5^{2} + (-5)^{2}}\]
to be clearer