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Evaluate the expression (4 - √(-25))(−4 + √(−16)) and write the result in the form a + bi. The real number...

Evaluate the expression (4 - √(-25))(−4 + √(−16)) and write the result in the form a + bi.
The real number a equals
The real number b equals

Answer

First, simplify the expression using imaginary numbers:

  1. √(-25) = 5i
  2. √(-16) = 4i

Substitute these into the expression:

(4 - 5i)(-4 + 4i)

Use the distributive property to expand:

  1. 4 * -4 = -16
  2. 4 * 4i = 16i
  3. -5i * -4 = 20i
  4. -5i * 4i = -20i² = 20 (since i² = -1)

Combine like terms:

-16 + 16i + 20i + 20 = 4 + 36i

Thus, the result is in the form a + bi where:

  1. The real number a equals 4
  2. The real number b equals 36

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