Question

Simplify the equation (-6+i)/(-5+i)

Answer 1

\(\large\color{black}{\displaystyle \frac{i-6}{i-5}}\)

Answer 2

multiply top and bottom times \(i+5\)

Answer 3

\(\large\color{black}{\displaystyle \frac{(i-6)\color{red}{\times (i+5)}}{(i-5)\color{red}{\times (i+5)}}}\)

Answer 4

don't we have to change the sign of `imaginary term ` ?

Answer 5

i^2-30/i^2-25?

Answer 6

Nnesha it doesn't matter at all:

\(a^2-b^2=(a-b)(a+b)\) will work to cancel the middle term with i to make the denominator a real number in either case.

Answer 7

Jmiliere, only the denominator is correct.

Answer 8

you forgot the MIDDLE TERM in the numerator

Answer 9

What middle term

Answer 10

\(\large\color{black}{ \displaystyle (i-6)(i+5)=i^2-6i+5i-30=i^2-i-30 }\)

Answer 11

So it's I-30/i^2-25

Answer 12

And if is \(i\) is here to denote \(\sqrt{-1}\), then you have:

\(\large\color{black}{ \displaystyle \frac{(\sqrt{-1}~)^2-i-30 }{(\sqrt{-1}~)^2-25} }\)

Answer 13

\(\large\color{black}{ \displaystyle \frac{-1-i-30 }{-1-25} }\)

Answer 14

hope you're good from here

Answer 15

31+I/24

Answer 16

are you sure that on the bottom is 24 ?

Answer 17

It would be 26 because of negatives

Answer 18

yes

\(\large\color{black}{ \displaystyle \frac{31+i }{26} }\)

Answer 19

Thank you!

Answer 20

Yw

Answer 21

ahh, I see. Answer would be the same. but i thought (have learned) we should multiply by the conjugate of the denominator which is -i-5.

Answer 22

-i-5 is same as -(i+5)....