Question

squer of √9+√40i+√9-√40i​

Answer 1

Answer:

Answer

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)