Simplify: Write answers in the form of a + bi, where a and b are real numbers.
(3-5i) (8-2i)
See examples posted by Breana
http://www.jiskha.com/display.cgi?id=1245724852
To simplify the expression (3-5i) * (8-2i) and write the answer in the form of a + bi, where a and b are real numbers, we will use the FOIL method.
FOIL stands for:
F - Multiply the First terms of each expression.
O - Multiply the Outer terms of each expression.
I - Multiply the Inner terms of each expression.
L - Multiply the Last terms of each expression.
Let's go step by step:
Step 1:
Multiply the First terms:
(3 * 8) = 24
Step 2:
Multiply the Outer terms:
(3 * -2i) = -6i
Step 3:
Multiply the Inner terms:
(-5i * 8) = -40i
Step 4:
Multiply the Last terms:
(-5i * -2i) = 10i^2
Now, let's combine the results:
24 - 6i - 40i + 10i^2
Notice that i^2 equals -1, so we can replace it in the expression:
24 - 6i - 40i + 10(-1)
Simplifying further:
24 - 6i - 40i - 10
Combine like terms:
(24 - 10) + (-6i - 40i)
14 - 46i
Therefore, the simplified form of (3-5i) * (8-2i) is 14 - 46i.