Question

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

Answer 1

Answer:

$Z = \frac{37i }{113 } - \frac{23}{113}$

Step-by-step 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:

$Z = \frac{5 + 9i}{8 + 7i}$

We rationalize to get:

$Z = \frac{5 + 9i}{8 + 7i} \times \frac{8 - 7i}{8 - 7i}$

We simplify to obtain:

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

This gives

$Z = \frac{37i - 23}{113 }$

Or

$Z = \frac{37i }{113 } - \frac{23}{113}$