Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Square root of $21-20i$ equals

Option 1)
$5-2i$

Option 2)
$5+2i$

Option 3)
$2+5i$

Option 4)
$2-5i$

Answers (1)

let $(a+ib)^{2}= 21-20i$

$a^{2}-b^{2}+i\left ( 2ab \right )= 21 -20i$

$a^{2}-b^{2}= 21$

and $2ab = -20$

$a^{2}-b^{2}= 21$

$ab=-10$

eliminating b = $\frac{-10}{a} in a^{2}-b^{2}=21$

we get

$a^{2}-100/a^{2}= 21\Rightarrow (a^{2})^{2}-21a^{2}-100=0$

$a^{2}=25$ or $a^{2}=-4$

$\therefore a= 5$ or $a= -5$

when a= 5 then b= -2 and when a =-5 b= 2

a+ib = 5-2i or -5+2i

Square Root of a Complex Number -

$\sqrt{z}=a+ib \ where\ z=x+iy \ is \ calcuated \ by\ equating\ real\ and \ imaginary \ parts \ of\ : \ x+iy=(a+ib)^2$

-

Option 1)

$5-2i$

This is correct

Option 2)

$5+2i$

This is incorrect

Option 3)

$2+5i$

This is incorrect

Option 4)

$2-5i$

This is incorrect

Posted by

Vakul

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Mains 2026 Registration LIVE: NTA session 1 application dates soon; exam, registration fee updates

anam-khan

JEE Mains 2026 Registration LIVE: NTA JEE session 1 application, exam dates soon; city choice available

anam-khan

JEE Main 2026 exam city option not removed: NTA dismisses viral claim

Latest Question