Question

Find the multiplicative inverse of 8+6i

Answer 1

Answer:

1/14 is the answer

Thank you

Answer 2

Multiplicative inverse of 8 + 6i is (4 - 3i)/50

Given :

The number 8 + 6i

To find :

The multiplicative inverse of 8 + 6i

Solution :

Step 1 of 2 :

Define multiplicative inverse of a number

1 is the Multiplicative identity

Let M ( ≠ 0 ) is the multiplicative inverse of N

Then M × N = 1 = N × M

⇒ M = 1/N

So 1/N is multiplicative inverse of N

Step 2 of 2 :

Find the multiplicative inverse of 8 + 6i

Let M be the multiplicative inverse of 8 + 6i

By the given condition

$\displaystyle \sf{ \implies M \times (8 + 6i) = 1}$

$\displaystyle \sf{ \implies M = \frac{1}{8 + 6i} }$

$\displaystyle \sf{ \implies M = \frac{(8 - 6i)}{(8 + 6i)(8 - 6i)} }$

$\displaystyle \sf{ \implies M = \frac{(8 - 6i)}{ {8}^{2} - {6}^{2} {i}^{2} } }$

$\displaystyle \sf{ \implies M = \frac{(8 - 6i)}{ {8}^{2} + {6}^{2} } }$

$\displaystyle \sf{ \implies M = \frac{(8 - 6i)}{ 64 + 36 } }$

$\displaystyle \sf{ \implies M = \frac{(8 - 6i)}{ 100 } }$

$\displaystyle \sf{ \implies M = \frac{(4 - 3i)}{ 50 } }$

The multiplicative inverse of 8 + 6i is (4 - 3i)/50