How to find the square root of -7-24i ?

1.	How to find the square root of -7-24i ?
Answer» Ans.\xa0Let\xa0{tex}\\sqrt {-7-24i} = x+yi{/tex}Squaring Both Sides,=> -7-24i = x2 - y2\xa0+ 2xyion comparing, we get=> x2 - y2\xa0= -7 ……(1)and 2xy = -24 ………(2)We know(x2+y2)2\xa0= (x2-y2)2\xa0+ 4x2y2=> (x2+y2)2 = 49 + 576=> (x2+y2)2\xa0= 625=> x2+ y2 = 25 …………(3)solving (2) and (3), We get{tex}x = \\pm 3 \\space \\space \\space and \\space y =\\pm4{/tex}from (2) as product of xy is -ve, so it means x and y are of opposite sign.So, when x = 3, y = -4when x = -3, y = 4Therefore,\xa0{tex}\\sqrt {-7-24i} = \\pm (3-4i){/tex}

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