Question

WILL GIVE MEDAL AND BECOME FAN.


Express in the form of " a+bi "
\[\large \bf \sqrt{i}+\sqrt{-i}\]

Answer 1

\[\large \bf \sqrt{i}+\sqrt{-i}\]

Answer 2

@hartnn

Answer 3

let me try

let
a+bi = sqrt i + sqrt(-i)

square both sides

Answer 4

a^2 - b^2 +2abi = i +i + 2sqrt (-i^2)

(a^2-b^2 ) + (2ab)i = 2i + 2

Answer 5

compare real and imaginary parts

ab =1
a^2-b^2 = 2

something seems wrong...

Answer 6

a^2 - b^2 +2abi = i -i + 2sqrt (-i^2)

(a^2-b^2 ) + (2ab)i = 0 + 2

Answer 7

yeah, so ab = 0
a^2-b^2 = 2

if b =0 ,
a^2 =2,
s = sqrt 2

Answer 8

hence
sqrt i + sqrt (-i) = sqrt 2 + 0i :)

Answer 9

wolf agrees :)
http://www.wolframalpha.com/input/?i=sqrt+i+%2B+sqrt%7B-i%7D

Answer 10

ask if any doubt in any step

Answer 11

oh!! thank you .. @hartnn

Answer 12

i got it