Question

(6-2i)^2 which is the coefficient of i ?

A.−24

B.−12

C.16

D.24

Answer 1

Option A: -24 is the coefficient of i

Step-by-step explanation:

The expression is
`(6-2 i)^(2)`

To determine the coefficient of i, first we shall find the square of the binomial for the expression
`(6-2 i)^(2)`

The formula to find the square of the binomial for this expression is given by

`(a-b)^(2)=a^(2)-2 a b+b^(2)`

where
`a=6` and
`b=2i`

Substituting this value and expanding, we get,

`(6-2 i)^(2)=6^(2) -2(6)(2i)+(2i)^(2)`

Simplifying the terms, we have,

`(6-2 i)^(2)=36-24i-4`

Thus, from the above expression the coefficient of i is determined as -24.

Hence, Option A is the correct answer.