Can someone explain how you get 8-6i out of (3-i)^2
Certainly! To find (3 - i)^2, we can use the formula for squaring a binomial. In general, (a - b)^2 can be simplified as follows:
(a - b)^2 = a^2 - 2ab + b^2
In our case, a = 3 and b = i. Substituting these values into the formula, we can calculate:
(3 - i)^2 = (3)^2 - 2(3)(i) + (i)^2
= 9 - 6i + i^2
Now, let's simplify the equation further. The term i^2 represents the square of the imaginary unit i. According to the definition, i^2 is equal to -1.
(3 - i)^2 = 9 - 6i + (-1)
= 8 - 6i
Therefore, (3 - i)^2 simplifies to 8 - 6i.