Question

simplify the expression sqrt of 1/(3+8i)-(2-5i)

Answer 1

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

Answer 2

\[A. \frac{ 3+i }{ 10 } \]
\[B. \frac{ -3+i }{ 10 }\]
\[C. \frac{ 3-i }{ 10 }\]
\[D. \frac{ (-3-i) }{ 10 }\]

Answer 3

@Michele_Laino hey, are you busy at all m8?

Answer 4

first step, we have to simplify the denominator:
\[\large \left( {3 + 8i} \right) - \left( {2 + 5i} \right) = 3 + 8i - 2 - 5i = \left( {3 - 2} \right) + \left( {8i - 5i} \right) = ...?\]
please continue

Answer 5

ok gimme a sec.

Answer 6

1 + 3i

Answer 7

that's right!

Answer 8

ok so how do we find the answer

Answer 9

so, we can write this:
\[\Large \frac{{\sqrt { - 1} }}{{(3 + 8i) - (2 + 5i)}} = \frac{{\sqrt { - 1} }}{{1 + 3i}}\]
now, we have to keep in mind that \(\sqrt{-1}=i\), so we have:
\[\Large \frac{{\sqrt { - 1} }}{{(3 + 8i) - (2 + 5i)}} = \frac{{\sqrt { - 1} }}{{1 + 3i}} = \frac{i}{{1 + 3i}}\]
next, second step:
I multiply both numerator and denominator by \(1+3i\), so, I get:
\[\Large \begin{gathered}
\frac{{\sqrt { - 1} }}{{(3 + 8i) - (2 + 5i)}} = \frac{{\sqrt { - 1} }}{{1 + 3i}} = \frac{i}{{1 + 3i}} = \hfill \\
\hfill \\
= \frac{{i\left( {1 - 3i} \right)}}{{\left( {1 + 3i} \right)\left( {1 - 3i} \right)}} \hfill \\
\end{gathered} \]

Answer 10

now, we have to simplify these quantities:
\[{i\left( {1 - 3i} \right)}=...?\]
and:
\[{\left( {1 + 3i} \right)\left( {1 - 3i} \right)}\]

Answer 11

oops.. I meant I multiply both numerator and denominator by \(1-3i\)

Answer 12

ok so the first one becomes \[1i - 3i^2\]

Answer 13

yes! and \(i^2=-1\) so we get:
\(i+3\)

Answer 14

then numerator is \(i+3\)

Answer 15

ok

Answer 16

oh wait lol

Answer 17

that's the answer

Answer 18

hahahah thanks a lot

Answer 19

no, please wait:
if I apply the distributive property, I get:
\[\left( {1 + 3i} \right)\left( {1 - 3i} \right) = 1\left( {1 - 3i} \right) + 3i\left( {1 - 3i} \right) = ...?\]
please continue

Answer 20

oh ok

Answer 21

ok so then you get \[1-9i?\]

Answer 22

I got \(1-9i^2\)

Answer 23

right my bad

Answer 24

which can be simplified to \(1-9(-1)=1+9=10\), since \(i^2=-1\)

Answer 25

so, the denominator is \(10\)

Answer 26

ok so the answer is \[(3+i)/10\]

Answer 27

yes! :)

Answer 28

thank you very much, have a nice day xx

Answer 29

:)