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

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

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Multiply numbers written in scientific notationright chevron icon

Full solution

Q. Multiply and simplify the following complex numbers:\newline(2−2i)⋅(4−4i) (2-2 i) \cdot(4-4 i)
  1. Apply distributive property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the two complex numbers.\newline(2−2i)∗(4−4i)=2⋅4+2⋅(−4i)+(−2i)⋅4+(−2i)⋅(−4i)(2-2i)*(4-4i) = 2\cdot 4 + 2\cdot (-4i) + (-2i)\cdot 4 + (-2i)\cdot (-4i)
  2. Perform multiplication for each term: Perform the multiplication for each term.\newline=8−8i−8i+8i2= 8 - 8i - 8i + 8i^2\newlineNote that i2=−1i^2 = -1.
  3. Substitute i2i^2 and combine like terms: Substitute i2i^2 with −1-1 and combine like terms.\newline= 8−8i−8i−88 - 8i - 8i - 8\newline= 8−16i−88 - 16i - 8
  4. Simplify expression by combining real and imaginary parts: Simplify the expression by combining the real parts and the imaginary parts.\newline=(8−8)−16i= (8 - 8) - 16i\newline=0−16i= 0 - 16i\newline=−16i= -16i

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