Show that if `iz^3+z^2-z+i=0`, then `|z|=1` – InterviewSolution

InterviewSolution

1.	Show that if `iz^3+z^2-z+i=0`, then `\|z\|=1`
Answer» We have `iz^(3) + z^(2) - z + i = 0` `rArr" "z^(3)-iz^(2)+iz + 1 = 0" "["on dividing both sides by I"]` `rArr" "z^(2)(z-i) + i(z-i) = 0` `rArr" "(z-i)(z^(2)+i)=0` `rArr" "z = i or z^(2) = -i`. Now, `z = i rArr \|z\| = \|i\| rArr \|z\| = 1` And, `z^(2) =-i rArr \|z^(2)\|=\|-i\|=1 rArr \|z\| = 1`.

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