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

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

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Multiply numbers written in scientific notationright chevron icon

Full solution

Q. Multiply and simplify the following complex numbers:\newline(−3−i)⋅(3+i) (-3-i) \cdot(3+i)
  1. Apply distributive property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the two complex numbers.\newline(−3−i)∗(3+i)=(−3)∗(3)+(−3)∗(i)+(−i)∗(3)+(−i)∗(i)(-3-i)*(3+i) = (-3)*(3) + (-3)*(i) + (-i)*(3) + (-i)*(i)
  2. Multiply terms: Multiply each term.\newline(−3)⋅(3)=−9(-3)\cdot(3) = -9\newline(−3)⋅(i)=−3i(-3)\cdot(i) = -3i\newline(−i)⋅(3)=−3i(-i)\cdot(3) = -3i\newline(−i)⋅(i)=−i2(-i)\cdot(i) = -i^2
  3. Evaluate i2i^2: Remember that i2i^2 is equal to −1-1.\newline−i2=−(−1)=1-i^2 = -(-1) = 1
  4. Combine like terms: Combine like terms.\newline−9+(−3i)+(−3i)+1=−9+1−3i−3i-9 + (-3i) + (-3i) + 1 = -9 + 1 - 3i - 3i
  5. Simplify the expression: Simplify the expression by adding/subtracting the real parts and the imaginary parts.\newline−9+1−3i−3i=−8−6i-9 + 1 - 3i - 3i = -8 - 6i

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