Question

conjugate of (- sqrt(2) + sqrt(3) * i)​

Answer 1

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Find the square root of 2+2

3

i.

Medium

Solution

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le (2+2

3

i)

1/2

=x+iy

sq. both side

2+2

3

i=x

2

−y

2

+2xyi

⇒x

2

−y

2

=2−−−−(i) & xy=

3

−−−−(ii)

we know

(x

2

+y

2

)

2

=(x

2

−y

2

)

2

+(2xy)

2

=2

2

+(2

3

)

2

=16

x

2

+y

2

=4−−−−(iii)

Solve (i) & (iii) from (2) & (iii)

2x

2

=16 2xy=2

3

x=±

3

x=±

3

∴ ⇒y=±1

Then,

(2+2

3

i)

1/2

=±(

3

+i)