Divide complex number by conjugate.

Thread starter js14
Start date Apr 24, 2011
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Complex Complex number Conjugate

In summary, a complex number is a number with a real and an imaginary part, often written as a + bi. The conjugate of a complex number has the same real part but the opposite sign for the imaginary part. Dividing by the conjugate simplifies complex fractions and removes the imaginary part from the denominator. To divide a complex number by its conjugate, we multiply both the numerator and denominator by the conjugate of the complex number in the denominator. This works for any complex number's conjugate, although the resulting fraction may not always simplify.

Apr 24, 2011

js14

divide complex number by conjugate. 1+3(sqrt-1)/ 2+(sqrt-1) The answer that i get is (5i/5)+1.
Is this correct?

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Apr 25, 2011

Mentallic

Homework Helper

Yes, and 5i/5=i

Related to Divide complex number by conjugate.

1. What is a complex number?

A complex number is a number that contains both a real and an imaginary part. It is often written in the form a + bi, where a is the real part and bi is the imaginary part.

2. What is the conjugate of a complex number?

The conjugate of a complex number is another complex number with the same real part, but the imaginary part has the opposite sign. For example, the conjugate of 3 + 4i is 3 - 4i.

3. Why do we need to divide by the conjugate of a complex number?

Dividing by the conjugate of a complex number allows us to simplify complex fractions and eliminate the imaginary part from the denominator.

4. How do we divide a complex number by its conjugate?

To divide a complex number by its conjugate, we multiply both the numerator and the denominator by the conjugate of the complex number in the denominator. This results in a real number in the denominator, making the fraction simpler to solve.

5. Can we divide by any complex number's conjugate?

Yes, we can divide by any complex number's conjugate. The resulting fraction may not always simplify, but the process of multiplying by the conjugate still applies.