What is the multiplicative identity of the complex number -4 + 8i?

Solution:

Given complex number is -4 + 8i

The multiplicative identity of any number whether real or imaginary is a number which when multiplied with the original number gives the result of unity.

In other words if the number is then its multiplicative inverse is 1/5 .

Then 5 multiplied by 1/5 gives the result as one.

Therefore the multiplicative identity of -4 + 8i is 1/(-4 + 8i)

Now 1/(-4 + 8i) can be rationalised to give multiplicative identity in another form

\(\frac{1}{-4 + 8i}\times \frac{-4 - 8i}{-4 - 8i}\)

\({-4 - 8i}\times \frac{1}{16 + 64}\)

-4/80 - 8i/80

-1/20 - i/10 is the multiplicative identity of -4 + 8i

What is the multiplicative identity of the complex number -4 + 8i?

Summary:

The multiplicative identity of the complex number -4 + 8i is -1/(-4 + 8i) or -1/20 i/10