Question

3+2i/6+5i simplify using i

Answer 1

Answer:

$\frac{28}{61}$ - $\frac{3}{61}$ i

Step-by-step explanation:

Given

$\frac{3+2i}{6+5i}$

Rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator

The conjugate of 6 + 5i is 6 - 5i, thus

= $\frac{(3+2i)(6-5i)}{(6+5i)(6-5i)}$ ← expand numerator / denominator using FOIL

= $\frac{18-3i-10i^2}{36-25i^2}$ → simplify using i² = - 1

= $\frac{18-3i+10}{36+25}$

= $\frac{28-3i}{61}$

= $\frac{28}{61}$ - $\frac{3}{61}$ i

Answer 2

Answer:

28 - 3i / 61

Step-by-step explanation:

Though the answer above is correct, in order to fit the layout of the question, the fraction has to be condensed.  If you insert the answer the way I typed it, it should be correct.

Hope this helps.