C is your answer because I did the answer when I went to the store to pick up my dog
The answer is -16 - 10i.
Using the distributive property on the first part, we have:
-2i*7--2i*4i + (3+i)(-2+2i)
-14i+8i² +(3+i)(-2+2i)
Using FOIL on the last part,
-14i+8i²+(3*-2+3*2i+i*-2+i*2i)
-14i+8i²-6+6i-2i+2i²
-10i+8i²-6+2i²
Since we know that i = -1,
-10i+8(-1)-6+2(-1)
-10i-8-6-2
-16-10i
5/6 because there are 5 possible possibilities and 6 numbers on the dice I'm assuming that the dice has 6 faces.
The answer is simple to work out you do 3/8 + 1/3
but the denominators are different so you find the lowest common multiple in this case 24 .
the frection is now 9/24 + 8/24 this is 17/24
I changed the fraction by doing this 24(common multiple) divided by 8 (denominator) that's how I got it if you don't understand just ask me
I assume each path
is oriented positively/counterclockwise.
(a) Parameterize
by

with
. Then the line element is

and the integral reduces to

The integrand is symmetric about
, so

Substitute
and
. Then we get

(b) Parameterize
by

with
. Then

and

Integrate by parts with



(c) Parameterize
by

with
. Then

and
