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:

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Example 3 - 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:

Click Here for Practice Problems
Example 4 - 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:

