What is negative seven 𝑖
multiplied by negative five plus five 𝑖?
We have a complex number negative
five plus five 𝑖 and we want to multiply it by a purely imaginary number negative
seven 𝑖. And we know that multiplying
complex numbers is just like multiplying algebraic expressions. Here, we can apply the distributive
property for expanding brackets. We multiply each part inside the
bracket by the number on the outside. That’s negative seven 𝑖 multiplied
by negative five which is 35𝑖 and negative seven 𝑖 multiplied by five 𝑖 which is
negative 35𝑖 squared.
And here, we recall the fact that
𝑖 is the solution to the equation 𝑥 squared equals negative one such that 𝑖
squared must be equal to negative one. So negative 35𝑖 squared is the
same as negative 35 multiplied by negative one which is simply 35. And since we now have a complex
number which is of course a result of adding a real and a purely imaginary number,
we write it as 35 plus 35𝑖.