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Evaluate the expression (-2 + i)(3 - 3i) and write the result in the form a + bi. The real number a equals...

Evaluate the expression (-2 + i)(3 - 3i) and write the result in the form a + bi.
The real number a equals
The real number b equals

Answer

To evaluate the expression (-2 + i)(3 - 3i), we use the distributive property (FOIL method):

  1. First: (-2) * 3 = -6
  2. Outer: (-2) * (-3i) = 6i
  3. Inner: (i) * 3 = 3i
  4. Last: (i) * (-3i) = -3i2 = 3 (since i2 = -1)

Combine these results:

-6 + 6i + 3i + 3 = -3 + 9i

So, the expression in the form a + bi is:

a = -3

b = 9

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