Simplify the expression?

Question

anonymous · Answer

attachment

anonymous · Answer

@jim_thompson5910 @.Sam.

hartnn · Answer

start by simplifying the denominator
combine like terms
$\Large (3-2i)+(1+5i) = 3+1 -2i+5i =...?$

anonymous · Answer

4-7i?

hartnn · Answer

$\Large -2i +5i = (-2+5)i = ... $

anonymous · Answer

and, we should eliminate the imaginary number from the denominator? so multiply the top and bottom by the conjugate?

hartnn · Answer

yes,
but its not 4-7i
try again

anonymous · Answer

sorry, um, 3i?

hartnn · Answer

yes!
4 +3i 

conjugate is 4-3i
multiply this in numerator and denominator

hartnn · Answer

simultaneously, you can do 

$\Large \sqrt{-9} = \sqrt{-1}\sqrt 9 = 3i$
got this ?

anonymous · Answer

no, i'm a little lost with that

hartnn · Answer

you know that 
$\Large i=\sqrt{-1}$
right ?

anonymous · Answer

yeah, i got that

hartnn · Answer

and we can split
$\Large \sqrt{ab} = \sqrt a \sqrt b$
thats what i did to -9

hartnn · Answer

$\sqrt{-9} = \sqrt{-1}\sqrt 9 = i \times 3 = 3i$

anonymous · Answer

so the square root of -9 is going to be equal to 3i?

anonymous · Answer

okay! and then we multiply 3i by 4-3i

hartnn · Answer

thats correct!

hartnn · Answer

that will give you the numerator
don't forget to simplify the denominator too

anonymous · Answer

i'm getting 12i - 9i for the numerator

anonymous · Answer

12-9i, rather

hartnn · Answer

isn't that 
$\Large 12i -9i^2$
?

hartnn · Answer

$4 \times 3i = 12 i \ -3i \times 3i = -9i^2$

anonymous · Answer

okay, and for the bottom is 16 - 12i + 12i - 9i^2

hartnn · Answer

we haven't completed numerator yet!

hartnn · Answer

$\Large i = \sqrt{-1}$
then what does 
$\Large i^2 = ... ?$

anonymous · Answer

just -1?

hartnn · Answer

thats correct!

so $\Large -9i^2 = -9 \times -1=...$

anonymous · Answer

9?

hartnn · Answer

right,
so replace $-9i^2$ of both numerator and denominator by 9

anonymous · Answer

i've never really looked at multiplying imaginary numbers by just what they mean, it's so much simpler like that. thank you!

hartnn · Answer

yes yes, imaginary/complex numbers is an easy topic ^_^

anonymous · Answer

so in the numerator, -9i^2 will be just 9, so 12i + 9
and in the denominator it'll be 16-9, so 7

anonymous · Answer

12i+9/7

hartnn · Answer

16-9 or 16+9
?

anonymous · Answer

whoops, positive 9, so 16+9

anonymous · Answer

12i+9/25

hartnn · Answer

yes

also , in generally we write the real part first,
instead of 12i +9, write 9+ 12i
and don't miss the brackets!

anonymous · Answer

thank you so much! i appreciate your time!

hartnn · Answer

most welcome ^_^