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Determine the value of z if,  z^2 + |z| = 0

Option: 1

0


Option: 2

i


Option: 3

-i


Option: 4

All options are correct


Answers (1)

best_answer

Let z = x+iy , then

\\\mathrm{x^2-y^2+2ixy+\sqrt{x^2+y^2}=0} \\\mathrm{Separating\; real\; and\; imaginary\; parts} \\\mathrm{x^2-y^2+\sqrt{x^2+y^2}=0} \\\mathrm{2xy = 0 \;\;\; ...(ii)} \\x=0 \,\,or\,\, y = 0\\\mathrm{When\;y\; =\; 0\; \; then} \\\mathrm{x^2+|x|=0 \Rightarrow x=0 \;} \\So, 0 + 0i = 0 \,is\,a\,solution\\\mathrm{When\; x=0 \;and\; putting\; in\; (i)} \\\mathrm{-y^2+|y|=0 \Rightarrow y=0 \;or\; y=\pm 1}\\So\,\, 0,i,-i\,are\,the\,solutions

 

 

On further verification we check x=0 only as x,y is from real

So z=0, i -i

 

Correct option is (d)

Posted by

Ritika Kankaria

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