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AP EAMCET · Maths · Complex Number

What is the modulus of the complex number \((1+2 i)(-2+i)\) ?

  1. A \(\sqrt{5}\)
  2. B 5
  3. C \(5 \sqrt{5}\)
  4. D \(\sqrt{35}\)
Verified Solution

Answer & Solution

Correct Answer

(B) 5

Step-by-step Solution

Detailed explanation

\(\begin{aligned} \mid(\hat{i} & +2 \hat{i}) \cdot(-2+\hat{i})|=| \hat{i}+2 i|\cdot|-2+i \mid \\ & =\left(\sqrt{1^2+2^2}\right) \cdot\left(\sqrt{(-2)^2+1^2}\right) \\ & =\sqrt{5} \times \sqrt{5}=5 . \end{aligned}\)