Question 100060
given the following two complex numbers, a=3+7i and b=-2-2i,calculate the following
a+b
a-b
a*b
a/b
Ok, for the most part, treat i like a variable. {{{a + b = 3 + 7i -2 - 2i}}}
{{{3 + 7i -2 - 2i = 1+5i}}}

{{{a - b = 3 + 7i -(-2 - 2i) = 3 + 7i + 2 + 2i = 5 + 9i}}}

a*b is just simply: {{{(3+7i)(-2-2i) = -6 - 6i - 14i - 14i^2}}}
Remember that i^2 = -1. So we simplify into: {{{-6 - 20i + 14 = 8 - 20i}}}

a/b is {{{(3+7i)/(-2-2i)}}} 
To simplify, you multiply the numerator and denominator by the denominator's complex conjugate which is -2+2i. 
{{{((3+7i)(-2+2i))/((-2-2i)(-2+2i))}}}
{{{(-6+6i-14i-14)/(4 -4i + 4i +4)}}}
{{{(-20-8i)/(8)}}}
{{{(4(-5-2i))/(8)}}}
{{{(-5-2i)/2}}}