Simplify (7-3i)^2.
So would I do this:
(7-3i) (7-3i)
then distribute it .... OR
(7-3i)^2
square everything 49+9i^2
? thanks
First option is correct.
It is of the form
(a-b)^2 = a^2 - 2ab + b^2
thank you, okay I wasn't' sure
To simplify the expression (7-3i)^2, you can follow these steps:
Step 1: Square the first term: (7)^2 = 49.
Step 2: Multiply the first term by the second term: 7 * (-3i) = -21i.
Step 3: Multiply the second term by the first term: (-3i) * 7 = -21i.
Step 4: Square the second term: (-3i)^2 = 9i^2.
Now, let's simplify the expression:
(7-3i)^2 = (49 - 21i - 21i + 9i^2)
In this step, when expanding the expression, you can combine like terms.
= (49 - 42i + 9i^2)
Now, simplify further:
We know that i^2 is equal to -1.
= (49 - 42i + 9(-1))
Multiply 9 by (-1):
= (49 - 42i - 9)
Combine like terms:
= (40 - 42i)
So, the simplified form of (7-3i)^2 is 40 - 42i.