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Multiply and simplify the following complex numbers: (-1-3i)*(-1+i)

Multiply and simplify the following complex numbers:\newline(−1−3i)⋅(−1+i) (-1-3 i) \cdot(-1+i)

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Full solution

Q. Multiply and simplify the following complex numbers:\newline(−1−3i)⋅(−1+i) (-1-3 i) \cdot(-1+i)
  1. Distribute terms: Distribute each term in the first complex number by each term in the second complex number.\newline(−1−3i)×(−1+i)=(−1×−1)+(−1×i)+(−3i×−1)+(−3i×i)(-1-3i) \times (-1+i) = (-1 \times -1) + (-1 \times i) + (-3i \times -1) + (-3i \times i)
  2. Calculate multiplications: Calculate each multiplication.\newline(−1×−1)=1(-1 \times -1) = 1\newline(−1×i)=−i(-1 \times i) = -i\newline(−3i×−1)=3i(-3i \times -1) = 3i\newline(−3i×i)=−3i2(-3i \times i) = -3i^2 (Remember that i2=−1i^2 = -1)
  3. Substitute and simplify: Substitute i2i^2 with −1-1 and simplify.\newline−3i2=−3(−1)=3-3i^2 = -3(-1) = 3
  4. Combine like terms: Combine like terms.\newline1+3+(−i+3i)=4+2i1 + 3 + (-i + 3i) = 4 + 2i

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