SOLUTION: show that and hence express d^4 as a function of i^3

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Question 1045480: show that
and hence express d^4 as a function of i^3
Found 3 solutions by josgarithmetic, ikleyn, advanced_Learner:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
1-d=1%2F%281%2Bi%29
1-1%2F%281%2Bi%29=d
d=%281%2Bi-1%29%2F%281%2Bi%29
d=i%2F%281%2Bi%29
d=%28i%2F%281%2Bi%29%29%28%281-i%29%2F%281-i%29%29
d=i%281-i%29%2F%282%29
d=%28i-i%5E2%29%2F2
d=%28i%2B1%29%2F2

d%5E4=%28%281%2Bi%29%2F2%29%5E4
d%5E4=%281%2Bi%29%5E4%2F16
d%5E4=%281%2F16%29%281%2Bi%29%5E2%281%2Bi%29%5E2

d%5E4=%281%2B4i%2B6%2Ai%5E2%2B4%2Ai%5E3%2Bi%5E4%29%2F16
d%5E4=%281-6%2B1%2B4i%2B4i%5E3%29%2F16
d%5E4=%28-4%2B4i%2B4i%5E3%29%2F16
highlight_green%28d%5E4=%28-1%2Bi%2Bi%5E3%29%2F4%29 ?

continuing....
d%5E4=%28i%5E2%2Bi%2Bi%5E3%29%2F4
i%28i%2B1%2Bi%5E2%29%2F4

Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.
I just answered couple days ago that this formulation is wrong and doesn't make sense.

Now I repeat it one more time . . . for those who . . .

Next time will redirect it into the TRASH section without explanations.


Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
show that %281%2Bi%29%281-d%29=1 and hence express d^4 as a function of i^3
solution
d=%28%28i%2B1%29%2F2%29
which is equivalent to
d=%281%2F2%29%2B%28i%2F2%29
and second part
d%5E4=%28i%5E3%29%2F%284i%29

.




check that
1%2Bi*(1-%28%281%2F2%29%2B%28i%2F2%29%29=1
1%2Bi*(1-%281%2F2%29-%28i%2F2%29=1
1%2Bi*(%281%2F2%29-%28i%2F2%29=1
1%2F2-%28i%2F2%29%2B%28i%2F2%29-%28i%5E2%29%2F%282%29=1
1%2F2-%28i%5E2%29%2F%282%29=1
1%2F2-%28-1%29%2F%282%29=1


since i%5E2=-1
1%2F2%2B%281%2F2%29=1
1=1