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  • Find the complex number satisfying the equation z+√2 |(z+1)|+i=0.

Find the complex number satisfying the equation z+\sqrt{2} |(z+1)|+i=0 .

Answers (1)

z+\sqrt{2} |(z+1)|+i=0\: \: \: \: ...(i)

Substituting z=x+iy   we get x+iy+\sqrt2 |x+iy+1|+i=0

x+i(1+y)+\sqrt2 \left [ \sqrt{(x+1)^2+y^2 } \right ]=0

x+i(1+y)+\sqrt2 \left [ \sqrt{(x^2+2x+1+y^2 ) } \right ]=0

1+y = 0

y = -1

x+\sqrt2 \sqrt{x^2+2x+2}=0

\sqrt2 \sqrt{x^2+2x+2}=-x

2x^2+4x+4=x^2

x^2+4x+4=0

(x+2)^2=0

x=-2

Hence,z=x+iy=-2-i

 

 

Posted by

infoexpert21

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