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 i^{2} = –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. |
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 i^{2} = –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 i^{2} = –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 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 i^{2} = –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 i^{2} = –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: |