WILL GIVE MEDAL AND BECOME FAN.

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

Question

WILL GIVE MEDAL AND BECOME FAN.

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

anonymous · Answer

$$\large \bf \sqrt{i}+\sqrt{-i}$$

anonymous · Answer

@hartnn

hartnn · Answer

let me try

let 
a+bi = sqrt i + sqrt(-i)

square both sides

hartnn · Answer

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

hartnn · Answer

compare real and imaginary parts

ab =1 
a^2-b^2 = 2

something seems wrong...

hartnn · Answer

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

hartnn · Answer

yeah, so ab = 0 
a^2-b^2 = 2

if b =0 ,
a^2 =2,
s = sqrt 2

hartnn · Answer

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

hartnn · Answer

hartnn · Answer

ask if any doubt in any step

anonymous · Answer

oh!! thank you .. @hartnn

anonymous · Answer

i got it