What is negative nine plus seven
plus four 𝑖 plus negative four minus four 𝑖 minus one plus three 𝑖?
Remember, we can add or subtract
complex numbers by adding their real parts and separately adding their imaginary
parts. Here we have four complex
numbers. Now it might not look like it, but
we could say that negative nine is actually a complex number. It’s negative nine plus zero
So to solve this problem, we’re
going to work out the real part first. That’s negative nine plus seven
minus four minus one, which is negative seven. Similarly, the imaginary parts are
zero, four, negative four, and negative three.
Remember, we distribute this final
set of parentheses. And a negative multiplied by a
positive is a negative. That gives us negative three. So the real part of our solution is
negative seven, and the imaginary part is negative three. So negative nine plus seven plus
four 𝑖 plus negative four minus four 𝑖 minus one plus three 𝑖 is negative seven
minus three 𝑖.
Now we also know that many
algebraic properties can be extended into the concept of negative numbers. We could actually have collected
like terms. Distributing that final set of
parentheses and then rearranging slightly, we get negative nine plus seven plus
negative four minus one plus four 𝑖 plus negative four 𝑖 minus three 𝑖, which
once again gives us negative seven minus three 𝑖. This latter method, the one of
collecting like terms, is generally the one that we use when adding and subtracting