Question

multiplicative inverse of 3+√4i ?

Answer 1

Step-by-step explanation:

$\text{Given: \( 3+\sqrt{4} i \) }$

$\text{To find : THE MULTIPLICATIVE INVERSE OF \( 3+\sqrt{4} i \)}$

$\text{LET \( z=3+\sqrt{4} i \)}$

$\text{ \( WE KNOW THAT IF 2 IS A COMPLEXNO THEN THE MULTIPLICATIVE INVERSE IS Given BY }$

$\text{\(Z ^{-1}=\frac{\overline{2}}{|2|^{2}} \)}$

$\begin{aligned} \therefore H & \forall R \in \quad z=3+i \sqrt{7} \\ \bar{z}=3-i \sqrt{7} &|2|^{2}=(3)^{2}+(\sqrt{4})^{2} \\|Z|^{2}=& 9+4=13 \end{aligned}$

$\therefore$ MULTIPLICATIVE INVERSE OF $3+\sqrt{7} i$ is Given BY $z^{-1}=\frac{3-\sqrt{4} i}{13}$

$=\frac{3}{13}-\frac{\sqrt{7}}{13} i$ HENCE THE MULTIPLICATIVE INVERSE OF $3+\sqrt{4} i$ is $\frac{3}{13}-\frac{\sqrt{4}}{13} i$