Question

Simplify. sqrt(x) = square root

3/sqrt(2) - 5i

Answer 1

Oh and i = imaginary number

Answer 2

\[\dfrac{3}{\sqrt 2} - 5i\] ?

Answer 3

Nope, -5i is also in the denominator

Answer 4

\[\frac{ 3 }{ \sqrt{2} -5i }\]

Answer 5

start off by rationalizing the denominator

Answer 6

Simple English please :D

Answer 7

Ah okay.

\[\dfrac{3}{\sqrt 2 - 5i}\]

So first thing to do is multiply both numerator and denominator by conjugate of denominator (\(\sqrt2 + 5i\)) Like this:

\[\dfrac{3}{\sqrt 2 - 5i}\cdot\dfrac{\sqrt2 + 5i}{\sqrt2 + 5i}\]

Answer 8

√2+5ı/9

Answer 9

\[\cdots=\dfrac{3(\sqrt2 + 5i)}{(\sqrt{2})^2-(5i)^2}\]

Answer 10

Now you just have integer in denominator. That's how you simplify.

Answer 11

Does that make sense? @voce

Answer 12

I got this as the final answer\[\frac{ 3\sqrt{2}+15i }{ 17 }\]

Answer 13

You mean \[\frac{ 3\sqrt{2}+15i }{ 27 }\]

You still have to simplify more. Note that numerator and denominator is divisible by 3.

Answer 14

\[\frac{ 3(\sqrt{2}+5i) }{ 3\cdot9 }\]

Answer 15

OH okay got you, thanks for your help

Answer 16

You are welcome