Question

Find the square root of 1-7i​

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)