Algebra-1

To divide the complex number (5 + 6i) by the conjugate of (2 - 3i), we will first identify the conjugate, then perform the division, and finally 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. A complex number is typically written in the form:

a + bi

where (a) is the real part and (b) is the imaginary part. The conjugate is given by:

a - bi

 

The conjugate of (2 - 3i) is:

2 + 3i

 

Step 2: Multiply by the Conjugate

Now we will divide (5 + 6i) by (2 + 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 (2 - 3i):

 

Step 4: Calculate the Numerator

First, we will calculate the numerator:

 

Calculating each term: