Question

sqrt(-25) / (5-2i)+(1-3i)

Answer 1

\[\frac{ \sqrt{-25} }{ (5-2i) + (1-3i) }\]

Answer 2

@jhonyy9 @ikram002p

Answer 3

@freckles

Answer 4

is it \[\frac{ -25 +30i }{ 61 }\]

Answer 5

sqrt(-25)
−−−−-------- =
(5−2i)+(1−3i)

how you have got it ?

Answer 6

sqrt(-25) = 5i

yes ?

Answer 7

cuz i first got

\[- \frac{ 5(5-6i) }{ 61 }\]

Answer 8

idk how to simplify that..

Answer 9

let 5-2i = a
and 1-3i = b

so than in denominator there are a+b
but you know what mean conjugate of something ?

Answer 10

yes.. to turn the symbol around.. so instead of - its +

Answer 11

hope you know formula a^2 -b^2 = (a-b)(a+b)

Answer 12

i do

Answer 13

than multiplie down and up by a-b - what will get ?

Answer 14

what do you mean ?

Answer 15

check what i have wrote above

Answer 16

im confused.

Answer 17

i dont understand what i have to do

Answer 18

(5−2i)+(1−3i) - this is the denominator
a + b

than multiplie down and up by a-b so you will get a^2 -b^2

what mean a^2 =(5-2i)^2 and
b^2 = (1-3i)^2

yes ?

Answer 19

yes i understand .

Answer 20

distribute parentheses -- see what will get - remain in denominator - what you need to make - try eliminate the terms with i from denominator

Answer 21

it looks a bit painful.
I would first add the bottom: reals to reals and imaginary to imaginary to get 1 complex number

can you do that ?

Answer 22

you mean like 6 - 5i ?

Answer 23

@phi

Answer 24

yes - so will be more easy

Answer 25

so than with 6-5i multiplie numerator and denominator by conjugate of 6-5i

do you know it ?

Answer 26

conjugate is 6 +5i but what do i multiply it with ?

Answer 27

yes

Answer 28

(6-5i)(6+5i) = ?

Answer 29

61?

Answer 30

yes

Answer 31

you multiply top and bottom by the conjugate 6+5i
the bottom is 36+25 = 61 (looks like that is what you got before)
the top is 5i(6+5i) = -25 +30i

Answer 32

so this will get for denominator

Answer 33

it looks like you did it correctly up top

Answer 34

soo the answer is correct.. its \[\frac{ -25 + 30i }{ 61 }\]

Answer 35

ok thank you

Answer 36

sometimes, people write it as -25/61 + 30/61 i
so that it is in real/imag format

Answer 37

was my pleasure -