(-3+6i)*(5-2i)

To multiply the complex numbers \((-3 + 6i)\) and \((5 - 2i)\), you can use the distributive property (also known as the FOIL method for binomials).

\[ (-3 + 6i)(5 - 2i) = (-3)(5) + (-3)(-2i) + (6i)(5) + (6i)(-2i) \]

Now, perform each multiplication:

1. \((-3)(5) = -15\)
2. \((-3)(-2i) = 6i\)
3. \((6i)(5) = 30i\)
4. \((6i)(-2i) = -12i^2\)

Since \(i^2 = -1\), we can replace \(-12i^2\) with \(12\):

Now, combine all those results:

\[ -15 + 6i + 30i + 12 \]

Combine the real parts and the imaginary parts:

1. Real part: \(-15 + 12 = -3\)
2. Imaginary part: \(6i + 30i = 36i\)

Thus, the final result of the multiplication is:

\[ -3 + 36i \]