I need math help. Step by step please. I don't want to cheat. Just help me solve the problem. Thanks.?

Question

(2/(2-3i) + (1/(1+i)

Answer 1

You need to simplify the i in the denominator by multiplying each by the complex conjugate of the denominator.

For the first term, 2/(2-3i), you should multiply the top and bottom by 2 + 3i to get (4 + 6i)/(13). You can figure out how to do the second term, and you should get (1+ i)/2.

Next put both terms under a common denominator, perhaps 26. Then you combine the two fractions. You should get (21 + 25i)/26

Answer 2

When confronted by complex numbers in the denominator, multiply by a unit fraction of the complex conjugate.
2/(2 - 3i) + (1/(1 + i) =
2(2 + 3i)/(2 - 3i)(2 + 3i) + 1(1 - i)/(1 + i)(1 - i) =
(4 + 6i)/(4 + 9) + (1 - i)/(1 + 1) =
(4 + 6i)/13 + (1 - i)/2 =
(2(4 + 6i) + 13(1 - i))/26 =
(8 + 12i + 13 - 13i)/26 =
(21 - i)/26

Answer 3

It depends on if i is a copmplec number or not. If it is multiply the top and bottom line of the first term by 2+3i (i.e. by 1) so it doesn't change value. This turns the denominator into an integer as it is the opposit of factoring x squared - a squared.

Do the same for the second term, this time the facor should be 1-i on the top and bottom.

Should be easy enough from there.

Answer 4

just like basic fractions - adding 1/4 + 1/3 , we have to get a common denominator
which is (2-3i)(1-i) as the above would have been 4 x 3 or 12
so we multiply 2/(2-3i) times (1+i)/(1+i) and
1/(1+i) times (2-3i)/(2-3i)

so 2(1-i)/(2-3i)(1+i) + 1(2-3i)/(2-3i)(1+i)=0
2-2i/(2-3i)(1+i) + (2-3i)/(2-3i)(1+i) =0
subtract one to get it on the other side
2-2i/(2-3i)(1+i) = - 2+3i/(2-3i)(1+i)
now multiply both sides by (2-3i)(1+i) which leaves us with the numerators
2-2i = -2+3i ...add 2 to both sides
2+2-2i = -2+2+3i
4-2i = 3i...add 2i to both sides
4-2i+2i = 3i+2i
4=5i....divide by 5
i = 4/5

i theenk - it is 2:22 am

Answer 5

(2/(2-3i) + (1/(1+i)

2/2-3i + 1/1+i

( cross multiple ) 2+i+2-3i

answer = 4-2i

Answer 6

ok so incredibly you opt for to get x by using itself. so right here is the final i will help: 2x+40+3x+27=one hundred eighty you opt for to pass the 40 and the 27 to the one hundred eighty part. you would be able to desire to subtract those 2 numbers fromt eh one hundred eighty so which you get 113. Then after that upload the 2x and the 3x mutually so which you get 5x. So now your situation must be 5x= 113. Now you opt for to get x by using itself so which you divide the 5 from x and 113. so which you answer must be x=22.6. right here is what it would look like: 2x+40+3x+27 = one hundred eighty 5x+sixty seven= one hundred eighty -sixty seven -sixty seven 5x = 113 ----- ----- 5 5 x = 22.6 i'm hoping this facilitates!