menu search
brightness_auto
Feel free to answer or ask any questions.
If you are new here please see how to use or FAQ.
more_vert
The imaginary part of $(3+2\sqrt{-54})^{1\over2}-(3-2\sqrt{-54})^{1\over2}$ can be

(1) $\sqrt{-6}$

(2) $\sqrt{6}$

(3) $-2\sqrt{6}$

(4) 6
thumb_up_off_alt 3 like thumb_down_off_alt 0 dislike

1 Answer

more_vert
 
done_all
Best answer

Ans. (3) $−2\sqrt6$

Sol. $|3+2\sqrt{-54}|=\sqrt{9+216}=15$

$\implies(3+2\sqrt{-54})^{1/2}=\pm\left(\sqrt{15+3\over2}+i\sqrt{15-3\over2}\right)$

$=\pm(3 + i\sqrt6)$

and $(3-2\sqrt{-54})^{1/2}=\pm(3-i\sqrt6)$

Hence $\left\{(3+2\sqrt{-54})^{1/2}-(3-2\sqrt{-54})^{1/2}\right\}$

$=\pm2i\sqrt6\text{ or }\pm6$

Hence imaginary part $=\pm2\sqrt6$

thumb_up_off_alt 1 like thumb_down_off_alt 0 dislike
Welcome to Jee Neet QnA, where you can ask questions and receive answers from other members of the community.

Most active Members

this week:
  1. AJINK Gupta's avatar AJINK Gupta1 points

1,101 questions

731 answers

345 comments

58 users

...