find the square root of 5+ 12i
Answers
Answered by
5
√5=2.23....
√12=3.46...
2.23+3.46
=5.69...
√12=3.46...
2.23+3.46
=5.69...
Answered by
8
sqrt (5+12i) = x+iy
=> 5+12i = x^2-y^2+2xyi
So, x^2-y^2 = 5 & 2xy = 12
=> (x+y)(x-y) = 5 & xy = 6
Now, (x+y)^2 = (x-y)^2 + 4xy
= 25/(x+y)^2 + 4×6
=> (x+y)^4 - 24 (x+y)^2 -25 = 0
=> [(x+y)^2 - 25] [(x+y)^2 + 1] = 0
Therefore, x+y = + 5, - 5 (Real values)
& (x-y) = + 1, - 1
So, x =3, -3 & y =2, -2
Reqd. answer is :
3+2i or, -3-2i
=> 5+12i = x^2-y^2+2xyi
So, x^2-y^2 = 5 & 2xy = 12
=> (x+y)(x-y) = 5 & xy = 6
Now, (x+y)^2 = (x-y)^2 + 4xy
= 25/(x+y)^2 + 4×6
=> (x+y)^4 - 24 (x+y)^2 -25 = 0
=> [(x+y)^2 - 25] [(x+y)^2 + 1] = 0
Therefore, x+y = + 5, - 5 (Real values)
& (x-y) = + 1, - 1
So, x =3, -3 & y =2, -2
Reqd. answer is :
3+2i or, -3-2i
suhanivadhera:
thank you for the explanation, helped a lot!
Similar questions