How do you simplify #(1 + 5i) (1 - 5i) #?

1 Answer
iceman
Jan 4, 2016

#(1+5i)(1-5i)=26#

Explanation:

#(1+5i)(1-5i)#
use the difference of squares formula:#(a-b)(a+b)=a^2-b^2#
so in this case:
#(1+5i)(1-5i)=(1)^2-(5i)^2#=>simplify:
#=1-(5^2*i^2)#=>simplify: #i^2=-1#:
#=1-(25*(-1))#
#=1-(-25)#
#=1+25#
#=26#

Or you may just use the FOIL method to distribute the parenthesis.
FOIL means First, Outside, Inside, Last:
#(1+5i)(1-5i)#
#=1-5i+5i-25i^2#
#=1+25#
#=26#

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