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The raising to the power of
a complex number is
carried out in exponential
form according to the rule:
i n

n in

z  (re )  r e ,
n

those the module is raised
to a power, and the
argument is multiplied by
the index of power
...


To extract a root from a
complex number, it is
necessary to convert it into
an exponential form:
i

z  re

and take into account that in
the general case the
argument is

  2k,

где k=0, 1, 2,…

Then the root of the complex
number will be equal to:
n

z  re
n

i (   2 k )



 re
n

  2k
i
n

From the obtained values of the
roots it is necessary to take the
first n values!!! (k=0,1,
...

The remaining values (при kn)
will be repeated
...

3

Answers to submit in
algebraic form
...

2

3
1
z 21 
i ;
2
2
3
1
z 22  
i ;
2
2

z 23  i
...
Raising a complex
number to a power and
extracting a root from it is
easier to produce in
exponential form
...
Extracting an n-th root
from a complex number
gives n different values

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