Question

Simplify the expression

Answer 1

\[\frac{ \sqrt{-1} }{ (4-3i)-(2+5i)}\]

Answer 2

you need to know a symbol for a weird number
\[\sqrt{-1}=i\]

Answer 3

you have an expression for difference of two complex numbers in the bottom
first start by simplifying that.

Answer 4

i did earlier and got 2-8i but i didn't know what to do with it

Answer 5

\[\frac{ \sqrt{-1} }{ (4-3i)-(2+5i)} = \dfrac{i}{2 -8i}\]

this is not in standard form yet

Answer 6

whats the conjugate of denominator ?

Answer 7

when you swithc the sign?

Answer 8

switch

Answer 9

2+8i?

Answer 10

yes flipping the sing of imaginary part gives you conjugate

Answer 11

yes we use conjugate to get rid off the i's in the denominator :

Answer 12

multiply top and bottom by 2+8i

Answer 13

i dont know what you get with i(2+8i)?

Answer 14

yes!

\[\begin{align}\frac{ \sqrt{-1} }{ (4-3i)-(2+5i)} &= \dfrac{i}{2 -8i} \\~\\
&= \dfrac{i}{2-8i}\color{Gray}{\times \dfrac{2+8i}{2+8i}} \\~\\
&= \dfrac{i\color{Gray}{(2+8i)}}{(2-8i)\color{Gray}{(2+8i)}} \\~\\
\end{align} \]

Answer 15

does it flip with (i)? like -8 + 21

Answer 16

2i

Answer 17

yes, \(i=\sqrt{-1}\) so \(i^2 = -1\)

Answer 18

ok so \[\frac{ -8+2i }{ 68 }\]

Answer 19

\[\begin{align}\frac{ \sqrt{-1} }{ (4-3i)-(2+5i)} &= \dfrac{i}{2 -8i} \\~\\
&= \dfrac{i}{2-8i}\color{Gray}{\times \dfrac{2+8i}{2+8i}} \\~\\
&= \dfrac{i\color{Gray}{(2+8i)}}{(2-8i)\color{Gray}{(2+8i)}} \\~\\
&= \dfrac{2i + 8i^2}{2^2 - (8i)^2} \\~\\
&= \dfrac{2i -8}{4+64} \\~\\

\end{align}
\]

Answer 20

Yes! just cancel the 2 top and bottomif you want..
its not so important though

Answer 21

\[\begin{align}\frac{ \sqrt{-1} }{ (4-3i)-(2+5i)} &= \dfrac{i}{2 -8i} \\~\\
&= \dfrac{i}{2-8i}\color{Gray}{\times \dfrac{2+8i}{2+8i}} \\~\\
&= \dfrac{i\color{Gray}{(2+8i)}}{(2-8i)\color{Gray}{(2+8i)}} \\~\\
&= \dfrac{2i + 8i^2}{2^2 - (8i)^2} \\~\\
&= \dfrac{2i -8}{4+64} \\~\\
&= \dfrac{-4+i}{34} \\~\\
&=-\dfrac{2}{17} + \dfrac{1}{34}i

\end{align}
\]

Answer 22

is it \[\frac{ -4+i }{ 34 }\]

Answer 23

i forgot to write the answer choices lol
15 - 8i / 49 -4 + i / 34 15 - 8i / 79 -4 + i / 4

Answer 24

looks good!

Answer 25

so B is right?

Answer 26

-4 + 1 / 34

Answer 27

(-4 + \(\color{red}{i}\)) / 34

Answer 28

yes

Answer 29

okkkk thank you so much. that's all i was stuck on, you're a great help! :)

Answer 30

and just turned this in and got a 100%, thanks again