Let` z= a+ ib` (where` a,b,in R` and` i = sqrt(-1)` such that `|2z+3i| = |z^(2)` identify the correct statement(s)?A. `|z|_("maximum")` is equal to `3`B. `|z|_("maximum")` is equal to `1`C. If `|z|_("maximum")` when `z=alpha + ibeta (alpha,beta in R and I = sqrt (-1) then (alpha^(3)+beta^(3))` is equal to `27`D. If `|z|_("maximum") "when" z= + iy (x,y in R "and" i = sqrt(-1) "then" (x^(2) +2y^(2))` is equal to 2`

Let` z= a+ ib` (where` a,b,in R` and` i = sqrt(-1)` such that `|2z+3i|

1.	Let` z= a+ ib` (where` a,b,in R` and` i = sqrt(-1)` such that `\|2z+3i\| = \|z^(2)` identify the correct statement(s)?A. `\|z\|_("maximum")` is equal to `3`B. `\|z\|_("maximum")` is equal to `1`C. If `\|z\|_("maximum")` when `z=alpha + ibeta (alpha,beta in R and I = sqrt (-1) then (alpha^(3)+beta^(3))` is equal to `27`D. If `\|z\|_("maximum") "when" z= + iy (x,y in R "and" i = sqrt(-1) "then" (x^(2) +2y^(2))` is equal to 2`
Answer» Correct Answer - A::B::C::D Given `\|2z+3i\| = \|z^(2)\|` ` because \|2z+3i\|le2\|z\|+3` `implies \|z\|^(2)le2\|z\|+3` `implies 0 le\|z\|le 3 " "...(1)` Again `\|2z+3i\|ge\|2\|z\|-3\|` `implies \|z\|^(2)ge\|2\|z\|-3\|` `therefore \|z\|ge1" " …..(2)` So,(1)`nn`(2)gives `1le\|z\|le3` Also,`\|z\|_("maximum")impliesz=3i` So, `alpha=0,beta=3` `&\|z\|("maximum") impliesz=-i` So,`x=0, y=-1`

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