Here are the step require to divide complex numbers:

 Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator. Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis. Step 3: Simplify the powers of i, specifically remember that i2 = –1. Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers. Step 5: Write you answer in the form a + bi. Step 6: Reduce your answer if you can.

Example 1 – Divide:

 Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator. Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis. Step 3: Simplify the powers of i, specifically remember that i2 = –1. Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers. Step 5: Write you answer in the form a + bi. Step 6: Reduce your answer if you can. In this case you can’t reduce, so the final answer is:

Example 2 – Divide:

 Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator. Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis. Step 3: Simplify the powers of i, specifically remember that i2 = –1. Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers. Step 5: Write you answer in the form a + bi. Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is: