Divide \$( - 6 + 8i)/ (- 3 + 4i)\$.

The given

\$( - 6 + 8i)/ (- 3 + 4i)\$

Find the conjugate of the denominator:

Conjugate of (- 3 + 4i) = - 3 - 4i

Multiply the numerator and the denominator by the conjugate of the denominator:

\$(- 6 + 8i)/(- 3 + 4i) times ((- 3 - 4i​)/(- 3- 4i))\$

Since \$i^2 = - 1\$.

Calculate the denominator and plug the \$i^2 = -1\$ and then simplify it:

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

\$ (a - b) ( a + b) = a^2 - b^2 \$

\$ 9 - 16i^2 = 9 - 16(-1) = 9 + 16 = 25\$

Calculate the numerator and plug the \$i^2 = -1\$ and then make it simplify:

\$(- 6 + 8i)(- 3 - 4i) \$

⇒ \$ - 6 times (- 3)+(- 6) times (- 4i) + 8i times (-3) + 8i times (- 4i)\$

⇒ \$ 18 + 24i - 24i - 32i^2\$

⇒ 18 - 32(-1)

⇒ 18 + 32

⇒ 50

Combine the results:

\$( - 6 + 8i)/ (- 3 + 4i) = \cancel(50)^2 / \cancel(25)\$

⇒ 2

Therefore, the division of complex numbers is 2.

Wrong: Because it does not match the result of dividing the two complex numbers. The correct result of the division is indeed 2, not 25

25

Option B is incorrect because it suggests the result is 5. This does not match the correct calculation

5

The complex numbers are accurately divided, confirming the result is correct

2

Option D represents the numerator of the fraction, not the final result after the division

50

Option

C

Can you summarize what you’ve understood in the above steps?