Question

if z=(1/2,1) then the value of z^-1 is​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{z=\left(\dfrac{1}{2},1\right)}$

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

$\mathsf{z^{-1}}$

$\underline{\textbf{Solution:}}$

$\textbf{Concept used:}$

$\textsf{The multiplicative inverrse of z = a+ib is}$

$\mathsf{z^{-1}=\dfrac{a-ib}{a^2+b^2}}$

$\mathsf{Here,\;\;z=\left(\dfrac{1}{2},1\right)}$

$\implies\mathsf{z=\dfrac{1}{2}+i}$

$\mathsf{Now,}$

$\mathsf{z^{-1}}$

$\mathsf{=\dfrac{\dfrac{1}{2}-i}{\left(\dfrac{1}{2}\right)^2+1^2}}$

$\mathsf{=\dfrac{\dfrac{1}{2}-i}{\dfrac{1}{4}+1}}$

$\mathsf{=\dfrac{\dfrac{1}{2}-i}{\dfrac{5}{4}}}$

$\mathsf{=\dfrac{4}{5}\left(\dfrac{1}{2}-i\right)}$

$\implies\boxed{\mathsf{z^{-1}=\dfrac{4}{5}\left(\dfrac{1}{2}-i\right)}}$

$\underline{\textbf{Find more:}}$

Answer 2

If Your question has 1/21 then the answer is in the photo then the answer here is 21

This is because the power here is -1 so you get the reciprocal hence the answer will be 21 as in the photo but you can also use a scientific calculator and get the answer directly