Question

Find the square root of 7-24i

Answer 1

Answer:

Step-by-step explanation:

Hii

Q)Find the square root of 7-24i :

Ans:-) (a+bi)(a+bi)=7-24i

a^2-b^2+2abi=7-24i

The real parts are equal, as are the real coefficients of the imaginary parts:

a^2-b^2=7

2abi=-24i

ab=-12==>a=-12/b Substituting we get:

(-12/b)^2-b^2=7

144/b^2-b^2=7

b^4+7b^2-144=0

(b^2+16)(b^2-9)=0

Since b is real b=3 or -3

a^2-9=7 ==> a^2=16 ==> a=+-4

Since ab=-12 one of a or b is negative.

So either of z=4-3i or z=-4+3i is a square root of 7-24i

(4-3i)(4-3i)=16-24i+9i^2=7-24i

.

Mark my ans as brainliest plz

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 ❣️