Question

find the square root of complex number 5 - 12i

Answer 1

Let the square root of the complex number be x+iy
so,
x+iy = √(5-12i)
Squaring both sides,

x^2 + (iy)^2 + 2xy i = 5 - 12 i
x^2 - y ^2 +2xyi = 5 -12

So, by comparing the real and imaginary parts on both sides of equation,

we get,

x^2 - y^2 = 5 and 2xy= -12 so, XY = -6

Now, put y = -6/x
we get,

x^2 - (-6/x)^2 = 5

x^2 - 36/x^2 = 5
x^4 - 5x^2 - 36 = 0
So,by factorizing

(x^2-9)(x^2+4) = 0

Now, x cannot be imaginary by the definition

So,
x^2 = 9 And thus, x= +-3

and thus, for x = 3
y = -6/3 = -2
and for x = -3
y = -6/-3 = 2

Thus the roots of (5-12i)
can be
(3-2i) or (-3+2i)

Answer 2

Answer:

Step-by-step explanation:

5_2i

5_2(2)

=1