Math, asked by Kumarabhishekjha, 1 year ago

Find the square root of 7-24i

Answers

Answered by jyashaswylenka
5

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

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Answered by Anonymous
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)

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