AP EAMCET · Maths · Complex Number
What is the modulus of the complex number \((1+2 i)(-2+i)\) ?
- A \(\sqrt{5}\)
- B 5
- C \(5 \sqrt{5}\)
- D \(\sqrt{35}\)
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \mid(\hat{i} & +2 \hat{i}) \cdot(-2+\hat{i})|=| \hat{i}+2 i|\cdot|-2+i \mid \\ & =\left(\sqrt{1^2+2^2}\right) \cdot\left(\sqrt{(-2)^2+1^2}\right) \\ & =\sqrt{5} \times \sqrt{5}=5 . \end{aligned}\)
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