    Question

# Let z=a+ib (where a,b ∈ R and i=√−1) such that |2z+3i|=|z2|. Identify the correct statement(s)?

A
|z|maximum is equal to 3.
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B
|z|minimum is equal to 1.
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C
If |z| is maximum, then a3+b3 is equal to 27.
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D
|z| is minimum, then (a2+2b2) is 2.
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Solution

## The correct options are A |z|maximum is equal to 3. B |z|minimum is equal to 1. C If |z| is maximum, then a3+b3 is equal to 27. D |z| is minimum, then (a2+2b2) is 2.|2z+3i|≤2|z|+3 |z|2≤2|z|+3 ⇒ 0≤|z|≤3−−−−(1) |2z+3i|≥|2|z|−3| |z2|≥|2|z|−3|⇒|z|≥1−−−−(2) So, (1) and (2) gives 1≤|z|≤3 |z|maximum⇒z=3i So, a=0, b=3 & |z|minimum⇒z=−i So, a=0, b=−1  Suggest Corrections  0      Similar questions  Related Videos   Solving Complex Equations
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