Question

E=IZ
Where E=(5+9i) and I=(8+7i)
How do I solve for Z?

Answer 1

`Z = (37i )/(113 ) - (23)/(113)`

Explanation:

We have the complex number relationship as:

E=IZ

Where E=(5+9i) and I=(8+7i)

We solve for Z to get;

Z=E/L

We then substitute the expressions to get:

`Z = (5 + 9i)/(8 + 7i)`

We rationalize to get:

`Z = (5 + 9i)/(8 + 7i) * (8 - 7i)/(8 - 7i)`

We simplify to obtain:

`Z = \frac{40 - 35i + 72i - 63}{ {8}^(2) + {7}^(2) }`

This gives

`Z = (37i - 23)/(113 )`

Or

`Z = (37i )/(113 ) - (23)/(113)`