The expression in the form of a + bi is 9-25i.
A complex number is characterized by an ordered pair of numbers, the real and imaginary parts. It can be represented in multiple ways such as Standard form(rectangular form), Polar form, Exponential form.
For the given situation,
The expression is (4-i) (-3+7i) - 7i(8+2i).
The expression can be simplified as
⇒ [tex](4-i) (-3+7i) - 7i(8+2i)[/tex]
⇒ [tex]4(-3)+28i+3i-7(i^{2} )-56i-14(i^{2} )[/tex]
⇒ [tex]-12-25i-7(-1)-14(-1)[/tex] [∵ [tex]i^{2} =-1[/tex]]
⇒ [tex]-12-25i+7+14[/tex]
⇒ [tex]9-25i[/tex]
Hence we can conclude that the expression in the form of a + bi is 9-25i.
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