Question

In the question: Find the square root of the complex no.: -7-24i I did'nt understand the step where x and y are squared in the 5th step

Answer 1

Well that squaring method is too lengthy and complicated... I have found an easy and short method to solve it..
1.focus on the coefficient of imaginary part...
2.half the coefficient of 'i'
3.now decompose that value into two factors, square of whose difference is your's coefficient of real part...
4.see the sign between real n imaginary part... And rewrite the two numbers (whose squares have been taken)...by inserting the sign between them...

Answer 2

ANSWER:-

$let \sqrt{ - 7 - 24i} = a + ib$

$- 7 - 24i = (a + ib {)}^{2} = {a}^{2} - {b}^{2} + 2iab$

$comparing \: coeffiecient \: we \: get$

${a}^{2} - {b}^{2} = - 7 \: \: and \: \: 2ab = - 24$

$ab = - 12$

$b = \frac{ - 12}{a}$

${a}^{2} - \frac{144}{ {a}^{2} } = - 7$

${a}^{2} + 7 {a}^{2} - 144 = 0$

$= > ( {a}^{2} - 9)( {a}^{2} + 16) = 0$

$Hence, {a}^{2} + 16≠0 \: \: \: so, {a}^{2} = 9$

$a = ±3$

$a = \frac{ - 12}{a} = ±4$

$for \: a = 3,b = - 4$

$a = - 3,b = - 4$

$so, = \sqrt{ - 7 - 24i} = ±(3 - 4i)$

HOPE IT'S HELPS YOU ❣️