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AP EAMCET · Maths · Complex Number

The real part of the complex number \(z=\frac{5+2 i}{2-5 i}-\frac{3-4 i}{4+3 i}-\frac{1}{i}\), is

  1. A \(2\)
  2. B \(0\)
  3. C \(3\)
  4. D \(4\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(0\)

Step-by-step Solution

Detailed explanation

\(z = \frac{(5+2 i)(2+5 i)}{2^2+5^2} - \frac{(3-4 i)(4-3 i)}{4^2+3^2} - \frac{1 \cdot (-i)}{i \cdot (-i)}\) \(z = \frac{10+25i+4i+10i^2}{4+25} - \frac{12-9i-16i+12i^2}{16+9} - (-i)\) \(z = \frac{29i}{29} - \frac{-25i}{25} + i\) \(z = i - (-i) + i\) \(z = i + i + i = 3i\)…