Dividing complex numbers might seem hard at first, but it gets easier when you follow some simple steps. Let’s make it clear!

Step-by-Step Guide to Dividing Complex Numbers

1. Know Your Complex Numbers: Imagine you want to divide two complex numbers: $z_1 = a + bi$ $z_2 = c + di$

2. Use the Conjugate: To get rid of the imaginary part in the bottom, we multiply the top and the bottom by the conjugate of the second number. The conjugate of $z_2$ is $c - di$. So, we have: $\frac{z_1}{z_2} = \frac{(a + bi)(c - di)}{(c + di)(c - di)}$

3. Multiply the Top Part: Now, let’s expand the top part: $(a + bi)(c - di) = ac - adi + bci + b d(-1) = (ac + bd) + (bc - ad)i$

4. Multiply the Bottom Part: For the bottom part, we simplify it like this: $(c + di)(c - di) = c^2 - (di)^2 = c^2 + d^2$

5. Put It All Together: Now you can put what you found together: $\frac{(ac + bd) + (bc - ad)i}{c^2 + d^2}$

6. Final Result: You can write this as: $= \frac{ac + bd}{c^2 + d^2} + \frac{bc - ad}{c^2 + d^2}i$

And there you go! Just follow these steps, and you can easily divide complex numbers whenever you want!