How do you expand #(z+1/z)^2#?

1 Answer
EZ as pi
Nov 14, 2016

#=z^2 +2 + 1/z^2#

Explanation:

Do not be put off by the fraction.

#(z +1/z)^2 = (z+1/z)(z+1/z)#

Multiply the 2 brackets - the FOIL method if you use it.

#(color(blue)(z)+color(red)(1/z))(z+1/z)#

#=color(blue)(z^2 +1) + color(red)(1+1/z^2)" "rarr cancelz/1 xx 1/cancelz = 1#

#=z^2 +2 + 1/z^2#

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