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NDA 2026
Exam
NDA
Year
2026
Subject
Mathematics
Chapter
Complex Number

NDA 2026 · Mathematics · Complex Number

Consider the following inequalities : I. 1+4i > 3+2i II. 2+3i III....

Consider the following inequalities :
I. 1+4i>3+2i1+4i > 3+2i
II. 2+3i<3+4i2+3i< 3+4i
III. 4+3i>3+4i4+3i > 3+4i
where i=−1i=\sqrt{-1}
How many of the above are valid ?

Options

  1. ANone
  2. BOne
  3. CTwo
  4. DAll the three

Correct answer

A. None

Step-by-step solution

The field of complex numbers cannot be ordered. Inequalities such as z1>z2z_1 > z_2 or z1<z2z_1 < z_2 are only defined if both z1z_1 and z2z_2 are purely real numbers.

Since all the given inequalities involve complex numbers with non-zero imaginary parts, they are mathematically meaningless.

Therefore, none of the given inequalities are valid.

Answer: None
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