Algebra-1

To divide the complex number (2 + 5i) by the conjugate of (1 + 3i), we will follow these steps: identify the conjugate, perform the division, and express the result in standard form.

Step 1: Find the Conjugate

The conjugate of a complex number is obtained by changing the sign of its imaginary part. For the complex number (1 + 3i), the conjugate is:

1 - 3i

 

Step 2: Set Up the Division

Now we will divide (2 + 5i) by (1 - 3i):

 

Step 3: Multiply by the Conjugate of the Denominator

To simplify the division, we multiply the numerator and denominator by the conjugate of the denominator, which is (1 + 3i):

 

Step 4: Calculate the Numerator

First, we will calculate the numerator:

 

Calculating each term:

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