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Question

If (-7-24i)12=x-iy, then x2+y2 is equal to


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Solution

Step 1. Remove square root part :

Given that (-7-24i)12=x-iy

Squaring on both sides

(-7-24i)=(x-iy)2

(-7-24i)=x2-2xyi-y2

Step 2. Equating real and imaginary part

x2-y2=-7 and

2xy=24

xy=242=12

As we know,

(x2+y2)2=(x2-y2)2+4x2y2=(-7)2+(2xy)2=49+(24)2=625

Taking Square root on both sides

(x2+y2)=25

Hence, the value of x2+y2 is 25.


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