Question

find the square root of 7 + 24 i​

Answer 1

Step-by-step explanation:

Let √−7+24i=x+iy

On squaring, we get

7+24i=(x2−y2)+2ixy

Equating the real and imaginary parts

x2−y2=−7 and 2xy=24

x2+y2 =√(x2−y2)+4x2y2

= √(−7)2+(24)2=25

Solving, x2−y2=−7 and x2+y2=25

we get x2=9 and y2=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)

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