Question

find the square root of (1-i)

Answer 1

\(\LARGE\color{blue}{ \bf \sqrt{1-i} }\) like this ?

Answer 2

you can't simplify this root.

Answer 3

yeah there is an answer in the book ..

Answer 4

The question here would be can you put whatever is in the square root as x^2, saying can you factor it in such a way that it's a perfect square.

For example,
\(\Large\color{blue}{ \bf \sqrt{2i} =\sqrt{(1+i)(1+i)}=\sqrt{(1+i)^2}=1+i }\)

but your's 1-i is not a perfect square.

Answer 5

@Darkk_Reaper - do you know that any complex number can be written in the form \(re^{i\theta}\) ?

Answer 6

no

Answer 7

what methods have you been taught for this kind of problem?

Answer 8

that would probably be too complicated... to write it as \(\large\color{blue}{ \bf re^{iθ} }\) I usually either find a simple root, or leave it as it is.

Answer 9

e.g. do you know any complex number can also be written in the form \(r(\cos(\theta)+i\sin(\theta)))\)

Answer 10

yeah

Answer 11

There is also a proof that shows that\[\cos(\theta)+i\sin(\theta)=e^{i\theta}\]If you know this then it simplifies this question

Answer 12

Otherwise you the methods shown here to solve this: http://www.mathcentre.ac.uk/resources/Engineering%20maths%20first%20aid%20kit/latexsource%20and%20diagrams/7_5.pdf

Answer 13

try it out - let me know if you get stuck and I'll try to explain it further

Answer 14

THANX DUDE

Answer 15

yw :)

Answer 16

yeah i have seen that , but how can i use those to solve this problem

Answer 17

let me formulate my thoughts on this as I would normally have solved this using \(re^{i\theta}\)

Answer 18

@Darkk_Reaper - do you know DeMoivre’s Theorem?

i.e. \((a + ib)^n=r^n(\cos(n\theta)+i\sin(n\theta))\)

Answer 19

SORRY