Question

find the modulus of 15-7i÷15+7i​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{\dfrac{15-7\,i}{15+7\,i}}$

$\underline{\textsf{To find:}}$

$\textsf{Modulus of the given complex number}$

$\underline{\textsf{Solution:}}$

$\textsf{Concept::}$

$\textsf{For any two complex numbers}\;\mathsf{z_1\;\&\;z_2}$

$\mathsf{|\dfrac{z_1}{z_2}|=\dfrac{|z_1|}{|z_2|}}$

$\textsf{Consider,}$

$\mathsf{|\dfrac{15-7\,i}{15+7\,i}|}$

$\mathsf{=\dfrac{|15-7\,i|}{|15+7\,i|}}$

$\mathsf{=\dfrac{\sqrt{15^2+(-7)^2}}{\sqrt{15^2+7^2}}}$

$\mathsf{=\dfrac{\sqrt{225+49}}{\sqrt{225+49}}}$

$\mathsf{=1}$

$\underline{\textsf{Answer:}}$

$\mathsf{|\dfrac{15-7\,i}{15+7\,i}|=1}$

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