Question

square root of
(-7+24i)​

Answer 1

Answer:

Let

−7+24i

=x+iy

On squaring, we get

−7+24i=(x

2

−y

2

)+2ixy

Equating the real and imaginary parts

x

2

−y

2

=−7 and 2xy=24

x

2

+y

2

=

(x

2

−y

2

)+4x

2

y

2

=

(−7)

2

+(24)

2

=25

Solving, x

2

−y

2

=−7 and x

2

+y

2

=25

we get x

2

=9 and y

2

=16

∴x=±3 and y=±4

Since xy is positive, x and y have the same sign.

∴(x=3,y=4) or (x=−3,y=−4)

∴

−7+24i

=(3+4i) or (−3−4i

Step-by-step explanation:

Hope helpful!?