Math, asked by kdjinx, 10 months ago

square root of 7+24i​

Answers

Answered by Anonymous
4

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 ❣️

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