Algebra-1

To find the result of multiplying the complex number (5 + 2i) by its conjugate, we first identify the conjugate of (5 + 2i).

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 (5 + 2i) is:

5 - 2i

 

Step 2: Multiply the Complex Number by Its Conjugate

Now, we will multiply (5 + 2i) by (5 - 2i):

(5 + 2i)(5 - 2i)

 

Using the formula for multiplying conjugates,