find the square root of a complex number root (7-24i)
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[tex] \tt{→ \sqrt{ - 7 - 24i} =x +iy }[/tex]
[tex] \tt{→ - 7 - 24i = (x + {iy)}^{2}}[/tex]
[tex] \tt{ →{x}^{2} - {y}^{2} = - 7}[/tex]
[tex] \tt{→2xy = - 24}[/tex]
[tex] \tt{→({x}^{2} + {y}^{2} )}^{2} = ( {x}^{2} - {y}^{2} ) {}^{2} + (2xy) {}^{2}
[/tex]
[tex] \tt{→(x + y) {}^{2} = 25 - (2)}[/tex]
[tex] \tt{→ {x}^{2} = 9 \: and \: \: {y}^{2} = 16 }[/tex]
[tex] \tt{→x = ±3 \: and \: y = ±4}[/tex]