Question 685129
Find the product of (4+5i) and (4-5i) What are pairs of complex numbers like these called?
These are called "conjugates" of each other because they are the same binomials with opposite signs in the middle.
You need to know that {{{highlight(i^2=-1)}}} then you can foil as always...but conjugates always multiply to be the difference of squares...so it is not necessary...but it works every time.
{{{(4+5i)(4-5i)}}}
{{{4(4-5i)+5i(4-5i)}}}
{{{16-20i+20i-25i^2}}}
{{{16-25i^2}}}
The above is the difference of squares that you can skip to for conjugates.
{{{16-25(-1)}}}
{{{16+25}}}
{{{highlight(41)}}}
Happy Calculating!!!