In summary, here is how you undertake the four operations with complex numbers. If you would like to go back to where we covered them in more depth click on the links below.
Addition and Subtraction
Multiplication
To multiply complex numbers, we follow the rules of algebraic conventions as well as remembering that $i\times i=-1$i×i=−1
Division
Division of complex numbers is carried out by multiplying by a fraction constructed using the conjugate of the denominator. This removes the complex component from the denominator.
Evaluate $\left(3+6i\right)+\left(7+3i\right)$(3+6i)+(7+3i).
Simplify $-6\left(3-5i\right)$−6(3−5i).
Simplify $-2i\left(4-3i\right)^2$−2i(4−3i)2, leaving your answer in terms of $i$i.
Find the value of $\frac{4+6i}{1+i}$4+6i1+i.