Simplify.
#1. 5(2-i) - 3(4+3i) ..my work:
10-5i-12-9i
-2-14i
Do you leave this as the answer or can you simplify it further?
#2. (2-i√2)²
1. Correct
2. What does the "*" mean?
To simplify the expression 5(2-i) - 3(4+3i), you correctly distributed the 5 and 3 to the terms in the parentheses. However, there was a mistake in your calculation. Let's correct it step by step:
5(2 - i) - 3(4 + 3i)
10 - 5i - 12 - 9i
When subtracting the quantities, you should subtract both the real parts and the imaginary parts separately:
(10 - 12) + (-5i - 9i)
-2 - 14i
Therefore, the correct simplified answer is -2 - 14i.
As for the second expression, (2 - i√2)², let's expand it step by step:
(2 - i√2)²
(2 - i√2)(2 - i√2)
To multiply these binomials, you can use the FOIL method (First, Outer, Inner, Last):
First: 2 × 2 = 4
Outer: 2 × -i√2 = -2i√2
Inner: -i√2 × 2 = -2i√2
Last: -i√2 × -i√2 = -(i√2)² = -(-2) = 2
Now, let's combine the terms:
4 - 2i√2 - 2i√2 + 2
6 - 4i√2
Therefore, the simplified form of (2 - i√2)² is 6 - 4i√2.