1

Problem

Divide the complex numbers: \$(6 + 3i) / (2 + i)\$.

2

Step

To divide the complex numbers

\$(6 + 3i) / (2 + i)\$

3

Step

We can use the process of multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of a complex number a + bi is a − bi.

4

Step

To find the conjugate of the denominator (2 + i), simply change the sign of the imaginary part to get 2 - i

\$(6 + 3i) / (2 + i) \times (2 - i) / (2 - i) \$

5

Step

Now, perform the multiplication in both the numerator and denominator:

\$ ( 12 - 6i + 6i - 3i^2 ) / ( 4 - 2i + 2i - i^2) = (12 - 3i^2) / (4 - i^2)\$

6

Step

Simplify terms with \$i^2\$ (where \$i^2 = -1\$), then simplify

\$ ( 12 + 3) / ( 4 + 1 )\$

7

Step

So, the result is

\$ (15) / 5 = 3 \$

8

Solution

So, the division of the complex numbers \$(6 + 3i) / (2 + i)\$ is equal to 3.

9

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

10

Choice-A

This is the accurate result of the division

Correct 3

11

Choice-B

This is wrong. The result of the division is not negative it’s a positive

Wrong -2

12

Choice-C

This is not correct because the calculation results in 3, not 6

Wrong 6

13

Choice-D

This is incorrect because, as we’ve shown, the division yields a non-zero complex number, specifically 3

Wrong 0

14

Answer

Option

A

15

Sumup

Please summarize choices