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

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

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Full solution

Q. Multiply and simplify the following complex numbers:\newline(−2−4i)⋅(1−i) (-2-4 i) \cdot(1-i) \newline+=− +\stackrel{-}{=}
  1. Apply distributive property: Apply the distributive property to multiply the complex numbers (−2−4i)(-2-4i) and (1−i)(1-i).\newline(−2−4i)(1−i)=(−2)(1)+(−2)(−i)+(−4i)(1)+(−4i)(−i)(-2-4i)(1-i) = (-2)(1) + (-2)(-i) + (-4i)(1) + (-4i)(-i)
  2. Calculate each multiplication: Calculate each multiplication separately.\newline(−2)⋅(1)=−2(-2)\cdot(1) = -2\newline(−2)⋅(−i)=2i(-2)\cdot(-i) = 2i\newline(−4i)⋅(1)=−4i(-4i)\cdot(1) = -4i\newline(−4i)⋅(−i)=4i2(-4i)\cdot(-i) = 4i^2
  3. Remember i2i^2 is −1-1: Remember that i2i^2 is equal to −1-1.\newline4i2=4∗(−1)=−44i^2 = 4*(-1) = -4
  4. Combine real and imaginary parts: Combine the real parts and the imaginary parts of the product. (−2)+(2i)+(−4i)+(−4)(-2) + (2i) + (-4i) + (-4)
  5. Simplify expression: Simplify the expression by combining like terms.\newlineReal parts: (−2)+(−4)=−6(-2) + (-4) = -6\newlineImaginary parts: (2i)+(−4i)=−2i(2i) + (-4i) = -2i
  6. Write final simplified form: Write the final simplified form of the product of the two complex numbers. −6−2i-6 - 2i

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