To simplify the expression 4 divided by (3 – 2i), we need to eliminate the imaginary unit i from the denominator. This can be approached by multiplying both the numerator and the denominator by the conjugate of the denominator.
The conjugate of (3 – 2i) is (3 + 2i). By multiplying by this conjugate, we can reformat the expression as follows:
Expression:
\( \frac{4}{3 – 2i} \times \frac{3 + 2i}{3 + 2i} \)
This multiplication gives:
Numerator:
\( 4 \times (3 + 2i) = 12 + 8i \)
Denominator:
\( (3 – 2i)(3 + 2i) = 3^2 – (2i)^2 = 9 – (-4) = 9 + 4 = 13 \)
Now we can combine these results:
So, the simplified expression is:
\( \frac{12 + 8i}{13} = \frac{12}{13} + \frac{8}{13}i \)
Thus, the final simplified form of the expression is:
Answer:
\( \frac{12}{13} + \frac{8}{13}i \)