Question

3+5i/-2+3i perform operation

Answer 1

Answer:

$\dfrac{9}{13}-\dfrac{19}{13}i$

Step-by-step explanation:

Remember $i^2=-1$

You are given the fraction $\dfrac{3+5i}{-2+3i}$

First, multiply the numerator and the denominator by -2-3i:

$\dfrac{3+5i}{-2+3i}=\dfrac{(3+5i)(-2-3i)}{(-2+3i)(-2-3i)}=\dfrac{(3+5i)(-2-3i)}{(-2)^2-(3i)^2}=\dfrac{(3+5i)(-2-3i)}{4-9i^2}=\dfrac{(3+5i)(-2-3i)}{4+9}$

This gives you 13 in denominator, now multiply two complex numbers in numerator:

$(3+5i)(-2-3i)=-6-9i-10i-15i^2=-6-19i+15=9-19i$

Thus, the initial fraction is

$\dfrac{9-19i}{13}=\dfrac{9}{13}-\dfrac{19}{13}i$