Question

Operations on Complex Numbers

Answer 1

simplify the expression

Answer 2

Ok so start by rewrite \[\sqrt{-10}=i \sqrt{10}\]

Answer 3

ok, im following

Answer 4

Do you get that idea?

Answer 5

yes I understand that i believe

Answer 6

Do the same with sqrt(-5)

Answer 7

Then distribute

Answer 8

ok so its i\[\sqrt{-5}\]

Answer 9

hang on

Answer 10

Not really, the reason for why you take out the i is that you want the minus under the squareroot to disappear

Answer 11

\[i \sqrt{5}\]

Answer 12

Do you know the definition of i?

Answer 13

\[i=\sqrt{-1}\]
\[i ^{2}=-1\]

Answer 14

well i know that i means the y on a plane and it is the imaginary part?

Answer 15

That's also, kind of, correct when dealing with imaginary numbers the Y-X plane is called Im-Re

Answer 16

So based on the definition of \[i=\sqrt{-1}\]
what's, for example \[\sqrt{-7}\]

Answer 17

?

Answer 18

\[i \sqrt{10}(11+i \sqrt{5})\]=\[11i \sqrt{10}+i ^{2}\sqrt{10}\sqrt{5}= 11i \sqrt{10}-\sqrt{50}\]