The multiplication of two complex numbers equals another complex number, we can find it with this formula:
[tex](a+bi)\times(c+di)=(ac-bd)+(ad+cd)i[/tex]From our complex numbers, a= -4, b=2, c=3, d= -7, then replacing these values into the above formula we get:
[tex]\begin{gathered} (-4+2i)\times(3-7i)=(-4\times3-2\times-7)+(-4\times-7+3\times-7)i \\ (-4+2i)\times(3-7i)=(-12-(-14))+(28+(-21))i \\ (-4+2i)\times(3-7i)=(-12+14)+(28-21)i \\ (-4+2i)\times(3-7i)=2+7i \end{gathered}[/tex]Then the product of these complex number equals 2+7i
