How do you find the product of the complex number: (5-2i)(5+2i)?
distribute the brackets using FOIL( or any method you use)
#(5 - 2i )(5 + 2i ) = 25 + 10i - 10i -4i^2 #
[ this process is useful in complex numbers as the product produces a real number - the 2nd bracket is the complex conjugate of the 1st and vice-versa.]
[ note :
# i^2 = (sqrt-1)^2 = -1 #]
#rArr(5-2i)(5+2i) = 25 + 10i - 10i +4 = 29color(black)(" a real number")#