Algebra-1

To divide the complex number (7 - 2i) by the conjugate of (3 + 4i), 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 (3 + 4i) is:

3 - 4i

 

Step 2: Set Up the Division

Now we will divide (7 - 2i) by (3 - 4i):

 

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 (3 + 4i):

 

Step 4: Calculate the Numerator

First, we will calculate the numerator:

 

Calculating each term: