Find the square root of -5 + 12 i.
aditya kashyap , 10 Years ago
Grade upto college level
Algebra> Find the square root of -5 + 12 i.
1 Answers
Latika Leekha
Last Activity: 10 Years ago
We are required to find the square root of -5 + 12i.
Let √(-5+12i) = x+iy
Then squaring both sides we get,
(-5+12i) = (x+iy)2
Hence, (-5+12i) = x2 – y2 + 2ixy
Comparing the real and imaginary parts on both the sides we have,
-5 = x2 – y2
and 12 = 2xy
Now, (x2 + y2)2 = (x2 – y2) 2 + 4x2y2
= (-5)2 + 122
= 169.
This gives (x2 + y2) = 13. (neglecting the negative sign as sum of squares of two numbers cannot be negative)
Hence, solving these two equations
-5 = x2 – y2 and (x2 + y2) = 13 we have
x2 = 4 and y2 = 9.
Now 12 = 2xy hence, the value of xy is positive which means that both x and y are of same sign.
Hence, the required answer is either (2, 3) or (-2, -3).
The square root of -5 + 12i is 
(2+3i).
Thanks & Regards
Latika Leekha
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