Find the multiplicative inverse of the complex number $$\sqrt{5}+3i$$

Asked by Pragya Singh | 1 year ago |  98

##### Solution :-

Let’s consider $$z = \sqrt{5} + 3i$$

Then,

$$\overline{z}= \sqrt{5} -3i$$ and

$$|z|^2=(\sqrt{5})^2+3^2=5+9=14$$

Thus, the multiplicative inverse of $$\sqrt{5} + 3i$$ is given by z-1

z-1 $$\dfrac{\overline{z}}{|z|^2}=\dfrac{ \sqrt{5} -3i}{14}$$

$$\dfrac{ \sqrt{5}}{14}-\dfrac{3i}{14}$$

Answered by Abhisek | 1 year ago

### Related Questions

#### Show that 1 + i10 + i20 + i30 is a real number?

Show that 1 + i10 + i20 + i30 is a real number?

#### Solve the quadratic equations by factorization method only 6x2 – 17ix – 12 = 0

Solve the quadratic equations by factorization method only 6x2 – 17ix – 12 = 0

#### Solve the quadratic equations by factorization method only x2 + (1 – 2i)x – 2i = 0

Solve the quadratic equations by factorization method only x2 + (1 – 2i)x – 2i = 0