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: Example 1

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 1
Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.
Step 2
Step 3: Simplify the powers of i, specifically remember that i2 = –1.
Step 3
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 4
Step 5: Write you answer in the form a + bi.
Step 5
Step 6: Reduce your answer if you can. In this case you can’t reduce, so the final answer is:
Step 6

  Example 2 – Divide: Example 2

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 1
Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.
Step 2
Step 3: Simplify the powers of i, specifically remember that i2 = –1.
Step 3
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 4
Step 5: Write you answer in the form a + bi.
Step 5
Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is:
Step 6

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Example 3 - Divide: Example 3

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 1
Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.
Step 2
Step 3: Simplify the powers of i, specifically remember that i2 = –1.
Step 3
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 4
Step 5: Write you answer in the form a + bi.
Step 5
Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is:
Step 6

Click Here for Practice Problems

Example 4 - Divide: Example 4

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 1
Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.
Step 2
Step 3: Simplify the powers of i, specifically remember that i2 = –1.
Step 3
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 4
Step 5: Write you answer in the form a + bi.
Step 5
Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is:
Step 6

Click Here for Practice Problems