Question

Find the product of the two complexnumbers. SHOW ALL WORK.(-4 + 2i)(3 - 7i) What’s the answer for this I am lost and confused it’s for a test please help me

Answer 1

The multiplication of two complex numbers equals another complex number, we can find it with this formula:

`(a+bi)*(c+di)=(ac-bd)+(ad+cd)i`

From our complex numbers, a= -4, b=2, c=3, d= -7, then replacing these values into the above formula we get:

`\begin{gathered} (-4+2i)*(3-7i)=(-4*3-2*-7)+(-4*-7+3*-7)i \\ (-4+2i)*(3-7i)=(-12-(-14))+(28+(-21))i \\ (-4+2i)*(3-7i)=(-12+14)+(28-21)i \\ (-4+2i)*(3-7i)=2+7i \end{gathered}`

Then the product of these complex number equals 2+7i