Simplify the expression in a+bi form.
(3+i)(5-2i)(4-7i)
a. 67-145i
b. 75-123i
c. 53-145i
d. 61-123i
Show me your expansion, and I will check it.
Did you remember that i^2 = -1 ?
I don't know how do to it. can you explain it to me?
if you can multiply binomials, you can multiply complex numbers. Start off with
(3+i)(5-2i)
= 3*5 - 3*2i + 5i - 2i^2
= 15 - 6i + 5i + 2 (since i^2 = -1)
= 17-i
Now multiply that by (4-7i) and you're done
Hi, I've just tried to work through this as you have and am really struggling. When I multiply by (4-7i) I get negative numbers?
maybe - what did you get?
take a look at
http://www.wolframalpha.com/input/?i=(3%2Bi)(5-2i)
and put in your numbers
To simplify the expression in (a+bi) form, we need to expand the given expression and combine like terms.
Step 1: Multiply the first two complex numbers (3+i)(5-2i):
(3+i)(5-2i) = 3(5) + 3(-2i) + i(5) + i(-2i)
= 15 - 6i + 5i - 2i^2
= 15 - i + 2
= 17 - i
Step 2: Multiply the result from step 1 with the third complex number (17-i)(4-7i):
(17-i)(4-7i) = 17(4) + 17(-7i) - i(4) - i(-7i)
= 68 - 119i - 4i + 7i^2
= 68 - 123i - 7
= 61 - 123i
Therefore, the simplified expression in (a+bi) form is 61 - 123i.
So the correct option is d. 61-123i.