Question

find the square root of a complex number root (7-24i)

Answer 1

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$\tt{→ \sqrt{ - 7 - 24i} =x +iy }$

$\tt{→ - 7 - 24i = (x + {iy)}^{2}}$

$\tt{ →{x}^{2} - {y}^{2} = - 7}$

$\tt{→2xy = - 24}$

$\tt{→({x}^{2} + {y}^{2} )}^{2} = ( {x}^{2} - {y}^{2} ) {}^{2} + (2xy) {}^{2} </p><p>$

$\tt{→(x + y) {}^{2} = 25 - (2)}$

$\tt{→ {x}^{2} = 9 \: and \: \: {y}^{2} = 16 }$

$\tt{→x = ±3 \: and \: y = ±4}$