Question

Find the multiplicative inverse of the complex number

4 3 - i .​

Answer 1

Step-by-step explanation:

the above picture showed the solution...

Answer 2

Given complex number :—

$\bold{z→} \: \bold{43 - i}$

We know that,

$\underline \mathtt{ Multiplicative \: inverse \: of \: the \: complex \: number \: \bold{ z}}$

$\large \bold{→ \frac{1}{z} }$

$→ \: \frac{1}{43 - i}$

$\bold{→ \frac{(43 + i)}{(43 - i)(43 + i)} }$

$\bold{→ \frac{43 + i}{ {43}^{2} - {i}^{2} } }$

$\bold{→ \frac{43 + i}{1849 - ( -1 )} }$

$\bold{→ \frac{43 + i}{1849 + 1} }$

$\bold{→ \frac{43 + i}{1850} }$

$\large\underline\bold{→ \frac{43}{1850} + i. \frac{1}{1850} }$