Question 13 of 47 What is the sum of the complex numbers below?

(5-8i) + (1-11i)

a. 6+19i
b. -6+19i
c. -6-19i
d. 6-19i​

d. 6-19i

Step-by-step explanation:

(5-8i)+(1-11i)

Step 1: Combine like terms within the parenthesis. There are no like terms within the parenthesis. So, drop the parenthesis and move on to the next step.

(Remember!! If you would have had a negative sign in front of either parenthesis, you would need to distribute out the negative sign).

5 - 8i + 1 - 11i

Step 2: Now add like terms.

5 + 1 - 8i - 11i

6 - 19i

You can't combine any more like terms, so this is your final answer.

6 - 19i

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.