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Multiply and simplify the following complex numbers: (-1+4i)*(4-3i)

Multiply and simplify the following complex numbers:\newline(−1+4i)⋅(4−3i) (-1+4 i) \cdot(4-3 i)

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Multiply numbers written in scientific notationright chevron icon

Full solution

Q. Multiply and simplify the following complex numbers:\newline(−1+4i)⋅(4−3i) (-1+4 i) \cdot(4-3 i)
  1. Distribute terms in complex numbers: Distribute each term in the first complex number by each term in the second complex number.\newline(−1+4i)∗(4−3i)=(−1⋅4)+(−1⋅−3i)+(4i⋅4)+(4i⋅−3i)(-1+4i)*(4-3i) = (-1\cdot 4) + (-1\cdot -3i) + (4i\cdot 4) + (4i\cdot -3i)
  2. Perform multiplication for each term: Perform the multiplication for each term.\newline(−1×4)=−4(-1\times 4) = -4\newline(−1×−3i)=3i(-1\times -3i) = 3i\newline(4i×4)=16i(4i\times 4) = 16i\newline(4i×−3i)=−12i2(4i\times -3i) = -12i^2
  3. Simplify using i2i^2: Remember that i2=−1i^2 = -1 and simplify the terms.\newline−12i2=−12∗(−1)=12-12i^2 = -12*(-1) = 12
  4. Combine like terms: Combine like terms.\newline(−4)+(3i)+(16i)+(12)=8+19i(-4) + (3i) + (16i) + (12) = 8 + 19i
  5. Write final answer in standard form: Write the final answer in the standard form of a complex number.\newlineThe product of the complex numbers (−1+4i)(-1+4i) and (4−3i)(4-3i) is 8+19i8 + 19i.

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