Question

If z=√37 + √-19 Find |Z|​

Answer 1

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

$\mathsf{z=\sqrt{37}+\sqrt{-19}}$

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

$\mathsf{|z|}$

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

$\textsf{Concept used:}$

$\textsf{The modulus or absolute value of the complex number z=a+ib is}$

$\mathsf{|z|=\sqrt{a^2+b^2}}$

$\textsf{Consider}$

$\mathsf{z=\sqrt{37}+\sqrt{-19}}$

$\textsf{This can be written as}$

$\mathsf{z=\sqrt{37}+\sqrt{-1}\sqrt{19}}$

$\mathsf{z=\sqrt{37}+i\,\sqrt{19}}$

$\textsf{Then,}$

$\mathsf{|z|=\sqrt{(\sqrt{37})^2+(\sqrt{19})^2}}$

$\mathsf{|z|=\sqrt{37+19}}$

$\mathsf{|z|=\sqrt{56}}$

$\mathsf{|z|=\sqrt{4{\times}14}}$

$\implies\boxed{\mathsf{|z|=2\sqrt{14}}}$

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