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Simplify the expression to a + bi form: (-12+2i)(-3+i) Answer:

Simplify the expression to a + bi form:\newline(−12+2i)(−3+i) (-12+2 i)(-3+i) \newlineAnswer:

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Full solution

Q. Simplify the expression to a + bi form:\newline(−12+2i)(−3+i) (-12+2 i)(-3+i) \newlineAnswer:
  1. Distribute Terms: Distribute each term in the first complex number by each term in the second complex number.\newline(−12+2i)(−3+i)=(−12×−3)+(−12×i)+(2i×−3)+(2i×i)(-12+2i)(-3+i) = (-12 \times -3) + (-12 \times i) + (2i \times -3) + (2i \times i)
  2. Perform Multiplication: Perform the multiplication for each term.\newline(−12×−3)=36(-12 \times -3) = 36\newline(−12×i)=−12i(-12 \times i) = -12i\newline(2i×−3)=−6i(2i \times -3) = -6i\newline(2i×i)=2i2(2i \times i) = 2i^2
  3. Apply i2i^2 Rule: Remember that i2=−1i^2 = -1, and apply this to simplify the term with i2i^2.\newline2i2=2(−1)=−22i^2 = 2(-1) = -2
  4. Combine Like Terms: Combine like terms. \newline36+(−12i)+(−6i)+(−2)=36−2−12i−6i=34−18i36 + (-12i) + (-6i) + (-2) = 36 - 2 - 12i - 6i = 34 - 18i
  5. Final Answer: Write the final answer in a+bia + bi form.\newlineThe simplified expression is 34−18i34 - 18i.

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