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Multiply and simplify the following complex numbers: (-4-5i)*(1-i)

Multiply and simplify the following complex numbers:\newline(−4−5i)⋅(1−i) (-4-5 i) \cdot(1-i)

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Full solution

Q. Multiply and simplify the following complex numbers:\newline(−4−5i)⋅(1−i) (-4-5 i) \cdot(1-i)
  1. Distribute terms: Distribute each term in the first complex number by each term in the second complex number.\newline(−4−5i)∗(1−i)=(−4)∗(1)+(−4)∗(−i)+(−5i)∗(1)+(−5i)∗(−i)(-4-5i)*(1-i) = (-4)*(1) + (-4)*(-i) + (-5i)*(1) + (-5i)*(-i)
  2. Multiply terms: Multiply the terms.\newline(−4)⋅(1)=−4(-4)\cdot(1) = -4\newline(−4)⋅(−i)=4i(-4)\cdot(-i) = 4i\newline(−5i)⋅(1)=−5i(-5i)\cdot(1) = -5i\newline(−5i)⋅(−i)=5i2(-5i)\cdot(-i) = 5i^2
  3. Simplify using i2i^2: Remember that i2=−1i^2 = -1 and simplify.\newline5i2=5∗(−1)=−55i^2 = 5*(-1) = -5
  4. Combine like terms: Combine like terms.\newline(−4)+(4i)+(−5i)+(−5)=−4−5+(4i−5i)=−9−i(-4) + (4i) + (-5i) + (-5) = -4 - 5 + (4i - 5i) = -9 - i

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