{√(9+4i)+√(9-4i)}² Find the value
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Answered by
0
Answer:
WER
Let x+iy=
9+40i
(x−iy)=9+40i
∴ x
2
+y
2
=9 (i)
and xy=20 (ii)
squaring (i) and adding with 4 times the square of (ii)
we get x
4
+y
4
−2x
2
y
2
+4x
2
y
2
=81+1600
⇒ (x
2
+y
2
)
2
=1681
⇒ x
2
+y
2
=41 (iii)
from (i)+(iii) we get x
2
=25
⇒ x=±5
and y
2
=16
⇒ y=±4
from equation (ii) we can see that
x & y are of same sign
∴ x+iy=(5+4i) or −(5+4i)
∴ sq. roots of 9+40i=±(5+4i)
±(5+4i)
Answered By
toppr
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