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Question

If the square root of -7+24iis x+iy then x is equal to


A

±1

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B

±2

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C

±3

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D

±4

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Solution

The correct option is C

±3


Explanation for the correct option

Given, square root of -7+24iis x+iy.

Let -7+24i=x+iy
On squaring, we get
-7+24i=x2-y2+2ixy
Equating the real and imaginary parts
x2-y2=-7and2xy=24x2+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
Hence, option C is correct.


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