Question

Its urgent....
can u solve...

if z = 4-3i ,find z^-1​

Answer 1

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

GIVEN :

Z = 4 - 3i

TO FIND :

z^-1

SOLUTION :

$\sf{z \: = \: 4 \: - \: 3i}$

$\sf{ \bar{z} \: = \: 4 + 3i}$

$\sf{ |z| \: = \: \sqrt{ {4}^{2} \: + \: {3}^{2} } }$

$= \: \sqrt{25}$

$= \: 5$

$\therefore \: \sf{ \: {z}^{ - 1} = \: \frac{ \bar{z}}{ |z| } }$

Putting the values from above, we get

$= \: \sf {\frac{4 \: + \: 3i}{ {5}^{2} } }$

$= \: \sf{\frac{4 \: + \: 3i}{25} }$

$= \: \sf{ \frac{4}{25} \: + \: \frac{3i}{25} }$

Hence our required answer is

$= \boxed{ \bf{ \: \sf{ \frac{4}{25} \: + \: \frac{3i}{25} }}}$

Answer 2

Given:- z = 4 - 3i

Find:- z^-1 = ?

$\sf\bar{z}$ = 4 + 3i

|z| = $\sf\sqrt{(4)^{2} + (3)^{2}}$

|z| = √25

|z| = 5

z^-1 = z bar / |z|

z^-1 = (4 + 3i)/5

z^-1 = (4/5) + (3i)/5