How to find the square root …
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Naveen Sharma 8 years, 9 months ago
Ans.
Let {tex}\sqrt {-7-24i} = x+yi{/tex}
Squaring Both Sides,
=> -7-24i = x2 - y2 + 2xyi
on comparing, we get
=> x2 - y2 = -7 ……(1)
and 2xy = -24 ………(2)
We know
(x2+y2)2 = (x2-y2)2 + 4x2y2
=> (x2+y2)2 = 49 + 576
=> (x2+y2)2 = 625
=> x2+ y2 = 25 …………(3)
solving (2) and (3), We get
{tex}x = \pm 3 \space \space \space and \space y =\pm4{/tex}
from (2) as product of xy is -ve, so it means x and y are of opposite sign.
So, when x = 3, y = -4
when x = -3, y = 4
Therefore,
{tex}\sqrt {-7-24i} = \pm (3-4i){/tex}
0Thank You