(-3,4+7)*(-1 7/18)

To multiply two complex numbers, you need to use the distributive property and remember that \( i^2 = -1 \).

Let's first convert the mixed number into an improper fraction:

\(-3,4+7 = -3 + \frac{4}{7} + 7 = -3+\frac{33}{7} = -3\frac{33}{7} \)

Now we can multiply the two complex numbers:

\((-3+4i) \times \left(-1\frac{7}{18} \right) = -3 \times -1 -3 \times \frac{7}{18} + \frac{33}{7} \times -1 + \frac{33}{7} \times \frac{7}{18}\)

Simplify each term:

\( = 3 + \frac{7}{6} - \frac{33}{7} - \frac{33}{18} \)

Now, we can add and subtract the fractions:

\( = 3 + \frac{7}{6} - \frac{33}{7} - \frac{11}{6} \)

Next, find a common denominator for the fractions:

\( = 3 + \frac{7 \times 7}{6 \times 7} - \frac{33 \times 6}{7 \times 6} - \frac{11}{6} \)

\( = 3 + \frac{49}{42} - \frac{198}{42} - \frac{11}{6} \)

Now, combine the fractions and simplify:

\( = 3 + \frac{49 - 198 - 231}{42} \)

\( = 3 - \frac{380}{42} \)

\( = 3 - \frac{190}{21} \)

Therefore, the product of \((-3+4i)\) and \(\left(-1\frac{7}{18} \right)\) is \(3 - \frac{190}{21}\).