Solve the equation z^4 + 81 = 0
Originally Posted by norivea
Taking the square root of both sides:
Again taking the square root of both sides:
=
So what is ?
To answer this, let's write "i" a bit differently using the exponential form for complex numbers:
Thus
= = =
Similarly:
= ... =
So finally the solution to is
= and
-Dan
Hello, norivea!
Solve the equation:
We have: .
The polar form of is: .
Then: .
Hence: . for
Therefore: .
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Alternate method
We have: .
. . Then: . and
Now, if you happen to know that: .
. . then we have: . and
which gives us the same fourth roots.