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Multiply and simplify the following complex numbers: (1-2i)*(4+i)

Multiply and simplify the following complex numbers:\newline(1−2i)⋅(4+i) (1-2 i) \cdot(4+i)

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Full solution

Q. Multiply and simplify the following complex numbers:\newline(1−2i)⋅(4+i) (1-2 i) \cdot(4+i)
  1. Distribute and Multiply: Distribute each term in the first complex number by each term in the second complex number.\newline(1−2i)∗(4+i)=1∗(4+i)−2i∗(4+i)(1-2i)*(4+i) = 1*(4+i) - 2i*(4+i)
  2. Combine Terms: Multiply the terms out.\newline1∗(4+i)=4+i1*(4+i) = 4 + i\newline−2i∗(4+i)=−2i∗4−2i∗i-2i*(4+i) = -2i*4 - 2i*i
  3. Simplify and Remember: Combine the results from Step 22.\newline(4+i)+(−8i−2i2)(4 + i) + (-8i - 2i^2)
  4. Combine Like Terms: Remember that i2=−1i^2 = -1 and simplify.\newline(4+i)+(−8i+2)=4+2+i−8i(4 + i) + (-8i + 2) = 4 + 2 + i - 8i
  5. Combine Like Terms: Remember that i2=−1i^2 = -1 and simplify.\newline(4+i)+(−8i+2)=4+2+i−8i(4 + i) + (-8i + 2) = 4 + 2 + i - 8i Combine like terms.\newline6−7i6 - 7i

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