Math, asked by sakshi281202, 10 months ago

Root(5+12i) + root(5-12i)/root(5+12i) -root(5-12i) =?

Answers

Answered by sprao53413
2

Please see

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Answered by Anonymous
1

let \sqrt{ - 5 + 12i}  = a + ib

 - 5 + 12i = (a + ib {)}^{2}  =  {a}^{2}  -  {b}^{2}  + 2iab

We \: will \: get \:  {a}^{2}  -  {b}^{2}  =  - 5, \: 2ab = 12

 {a}^{2}  -  \frac{36}{ {a}^{2} }  =  - 5.......b =  \frac{6}{a}

 {a}^{4}  + 5 {a}^{2}  - 36 = 0

( {a}^{2} - 4)( {a}^{2}   + 9) = 0

a = ±2 \: and  \: ±3

we \: have \: a = 2 \: and \: b = 3

a =  - 2 \: and \: b =  - 3

b =  \frac{6}{a}  = ±3 so \sqrt{ - 5 + 12i}

 = ±(2 + 3i)

hope it's helps you ❤️

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