What is the value of #root5 -1#?
3 Answers
see below
Explanation:
Since,
Similarly,
Explanation:
Consider other roots of
If the radicand is negative, the root must have been a negative number, raised to an odd power.
It depends...
Explanation:
The expression
As a real valued function of reals,
#(-1)^5 = -1#
and hence:
#root(5)(-1) = -1#
As a complex valued function of complex numbers,
#e^(pi/5i) = 1/4(1+sqrt(5))+1/4sqrt(10-2sqrt(5))i#
#e^((3pi)/5i) = 1/4(1-sqrt(5))+1/4sqrt(10+2sqrt(5))i#
#e^(pii) = -1#
#e^((7pi)/5i) = 1/4(1-sqrt(5))-1/4sqrt(10+2sqrt(5))i#
#e^((9pi)/5i) = 1/4(1+sqrt(5))-1/4sqrt(10-2sqrt(5))i#
The first of these can be considered the principal complex fifth root of