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Multiply and simplify the following complex numbers: (-2+4i)*(5+i)

Multiply and simplify the following complex numbers:\newline(−2+4i)⋅(5+i) (-2+4 i) \cdot(5+i)

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Multiply numbers written in scientific notationright chevron icon

Full solution

Q. Multiply and simplify the following complex numbers:\newline(−2+4i)⋅(5+i) (-2+4 i) \cdot(5+i)
  1. Distribute terms: Distribute each term of the first complex number by each term of the second complex number.\newline(−2+4i)∗(5+i)=(−2⋅5)+(−2⋅i)+(4i⋅5)+(4i⋅i)(-2+4i)*(5+i) = (-2\cdot 5) + (-2\cdot i) + (4i\cdot 5) + (4i\cdot i)
  2. Multiply terms: Multiply the terms.\newline(−2×5)=−10(-2 \times 5) = -10\newline(−2×i)=−2i(-2 \times i) = -2i\newline(4i×5)=20i(4i \times 5) = 20i\newline(4i×i)=4i2(4i \times i) = 4i^2
  3. Simplify i2i^2: Remember that i2=−1i^2 = -1 and simplify.\newline4i2=4∗(−1)=−44i^2 = 4*(-1) = -4
  4. Combine like terms: Combine like terms.\newline(−10)+(−2i)+(20i)+(−4)(-10) + (-2i) + (20i) + (-4)
  5. Add real and imaginary parts: Add the real parts and the imaginary parts separately.\newlineReal parts: −10+(−4)=−14-10 + (-4) = -14\newlineImaginary parts: −2i+20i=18i-2i + 20i = 18i
  6. Write final answer: Write the final answer as a complex number. −14+18i-14 + 18i

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