AP EAMCET · Maths · Complex Number
If \((3+4 i)^{2025}=5^{2023}(x+i y)\), then \(\sqrt{x^2+y^2}=\)
- A 5
- B 25
- C 125
- D 625
Answer & Solution
Correct Answer
(B) 25
Step-by-step Solution
Detailed explanation
\\(|(3+4 i)^{2025}| = |5^{2023}(x+i y)|\\) \\(|3+4i|^{2025} = 5^{2023}|x+i y|\\) \\((\\sqrt{3^2+4^2})^{2025} = 5^{2023}\\sqrt{x^2+y^2}\\) \\(5^{2025} = 5^{2023}\\sqrt{x^2+y^2}\\) \\(\\sqrt{x^2+y^2} = \\frac{5^{2025}}{5^{2023}}\\) \\(\\sqrt{x^2+y^2} = 5^{2025-2023}\\)…
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