The expression (3-7i)^2 is equivilant to? i know what the answer is im just not sure how to get it please help
Just expand it
(3-7i)^2
= (3-7i)(3-7i)
= 9 - 42i + 49i^2 , but i^2 = -1
= 9 - 42i - 49
= -40 - 42i
okay thank you
To find the equivalent of (3-7i)^2, you need to square the expression.
Using the formula (a - b)^2 = a^2 - 2ab + b^2, you can expand (3-7i)^2 as follows:
(3-7i)^2 = (3-7i)(3-7i)
= 3(3) + 3(-7i) - 7i(3) - 7i(-7i)
= 9 - 21i - 21i + 49i^2
Since i^2 is equal to -1, you can simplify further:
9 - 21i - 21i + 49i^2
= 9 - 42i + 49(-1)
= 9 - 42i - 49
= -40 - 42i
Therefore, the equivalent of (3-7i)^2 is -40 - 42i.
To find the equivalent expression for the given expression (3-7i)^2, we can use the binomial expansion.
Step 1: Expand the expression using the formula (a+b)^2 = a^2 + 2ab + b^2.
So, (3-7i)^2 = (3)^2 + 2(3)(-7i) + (-7i)^2
Step 2: Simplify each term in the expanded expression.
(3)^2 = 9
2(3)(-7i) = -42i
(-7i)^2 = (-7)^2(i)^2 = 49(-1) = -49
Step 3: Combine the simplified terms to get the final result.
(3-7i)^2 = 9 - 42i - 49
= -40 - 42i
Therefore, the equivalent expression for (3-7i)^2 is -40 - 42i.