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Multiply and simplify the following complex numbers: (3-4i)*(-3+2i)

Multiply and simplify the following complex numbers:\newline(3−4i)⋅(−3+2i) (3-4 i) \cdot(-3+2 i)

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Full solution

Q. Multiply and simplify the following complex numbers:\newline(3−4i)⋅(−3+2i) (3-4 i) \cdot(-3+2 i)
  1. Distribute terms: Distribute each term in the first complex number by each term in the second complex number.\newline(3−4i)⋅(−3+2i)=3⋅(−3)+3⋅(2i)−4i⋅(−3)−4i⋅(2i)(3-4i)\cdot(-3+2i) = 3\cdot(-3) + 3\cdot(2i) - 4i\cdot(-3) - 4i\cdot(2i)
  2. Multiply terms: Multiply the terms.\newline3⋅(−3)=−93 \cdot (-3) = -9\newline3⋅(2i)=6i3 \cdot (2i) = 6i\newline−4i⋅(−3)=12i-4i \cdot (-3) = 12i\newline−4i⋅(2i)=−8i2-4i \cdot (2i) = -8i^2
  3. Combine like terms: Combine like terms and remember that i2=−1i^2 = -1.\newline−9+6i+12i−8(−1)=−9+18i+8-9 + 6i + 12i - 8(-1) = -9 + 18i + 8
  4. Simplify expression: Simplify the expression by adding real parts and imaginary parts separately.\newline−9+8=−1-9 + 8 = -1 (Real part)\newline18i18i (Imaginary part)
  5. Write final answer: Write the final answer as a complex number. −1+18i-1 + 18i

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