Power of Iota
Power
of Iota:
Sometimes there may be
asked problems in which higher powers of iota are involved. So , in such cases
remember a key fact that :
ü "
Iota raised to power 4 or a multiple of 4 always equals unity i.e : 1
."
Keeping
in mind this thing, very huge powers of iota can be simplified in a matter of seconds.
For example :
* iota raised to power
51 = (iota to 48) x (iota to 3) *
Now " iota to 48
is unity as 48 is a multiple of 4 and iota to 3 is just minus iota."
So
finally , * Iota to 51 = negative iota = - i.
Another interesting
trend regarding powers of iota can be observed in such a way that:
ü " If we add four consecutive powers of
iota then the sum equals zero."
For
example :
* iota to 4
+ iota to 5 + iota to 6 + iota to 7 = 0 *
This
trick even works when the powers are negative. :)
Similarly
in case of multiplication :
ü " Product of four consecutive powers
of iota equals negative of unity."
For example :
* (iota to 9)(iota to
10)(iota to 11)(iota to 12) = -1*
This trick also works
even if the powers are negative. :)
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Keeping
in mind these tricks try to solve following problems as quickly as you can.
§
Problem Set.
1.
Iota
raised to power 332.
2. Iota
raised to the power -33.
3.
Negative
unity raised to the power (23/2).
4.
iota
to (97) + iota to (98) + iota to (100) + iota to (99) = ?
.
5.
iota
to (-32) + iota to (-29) + iota to (-31) + iota to (-30) = ?.
6.
iota
to (-1) + iota to (-2) + iota to (-3) + iota to (-4) + iota to
(-5) = ?.
7.
(iota
to 1)(iota to 2)(iota to 0)(iota to -1) = ?
8.
(iota
to 30)(iota to 32)(iota to 29)(iota to -1)(iota to 31) = ?
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§
Solution Set:
1. Unity ; 2. Negative
iota ; 3. Negative of iota ;
4. Zero ; 5. Zero ;
6. Negative of iota ; 7. Negative of Unity ;
8. Iota.
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