Answer :
Since the brackets are
[tex](1-9i)(1-4i)(4-3i)[/tex]We will start to multiply the first 2 brackets, then multiply the answer by the 3rd bracket
[tex]\begin{gathered} (1-9i)(1-4i) \\ 1st\times1st=1\times1=1 \end{gathered}[/tex][tex]1st\times2nd=1\times(-4i)=-4i[/tex][tex]2nd\times1st=-9i\times1=-9i[/tex][tex]2nd\times2nd=-9i\times(-4i)=36i^2[/tex]The value of i^2 is -1, then
[tex]36i^2=-36[/tex]The answer to the product is
[tex](1-9i)(1-4i)=1-4i-9i-36[/tex]Add the like terms
[tex](1-9i)(1-4i)=(1-36)+(-4i-9i)=(-35-13i)[/tex]Now let us multiply the 3rd bracket by the answer
[tex]\begin{gathered} (4-3i)(-35-13i) \\ 1st\times1st=4\times-35=-140 \end{gathered}[/tex][tex]1st\times2nd=4\times(-13i)=-52i[/tex][tex]2nd\times1st=-3i\times(-35)=105i[/tex][tex]2nd\times2nd=-3i\times-13i=39i^2=-39[/tex]Now write them together and add the like terms
[tex]\begin{gathered} -140+(-52i)+(105i)+(-39)= \\ (-140-39)+(-52i+105i)= \\ -179+53i \end{gathered}[/tex]The product of the 3 brackets is -179 + 53i