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

Multiply and simplify the following complex numbers:\newline(−2+2i)⋅(5+5i) (-2+2 i) \cdot(5+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+2i)⋅(5+5i) (-2+2 i) \cdot(5+5 i)
  1. Apply distributive property: Apply the distributive property (FOIL method) to multiply the two complex numbers.\newline(−2+2i)∗(5+5i)=(−2⋅5)+(−2⋅5i)+(2i⋅5)+(2i⋅5i)(-2+2i)*(5+5i) = (-2\cdot 5) + (-2\cdot 5i) + (2i\cdot 5) + (2i\cdot 5i)
  2. Perform multiplication for each term: Perform the multiplication for each term.\newline(−2×5)=−10(-2 \times 5) = -10\newline(−2×5i)=−10i(-2 \times 5i) = -10i\newline(2i×5)=10i(2i \times 5) = 10i\newline(2i×5i)=10i2(2i \times 5i) = 10i^2
  3. Simplify term with i2i^2: Remember that i2=−1i^2 = -1 and apply this to simplify the term with i2i^2.\newline10i2=10∗(−1)=−1010i^2 = 10*(-1) = -10
  4. Combine like terms: Combine like terms.\newline(−10)+(−10i)+(10i)+(−10)=−10−10−10i+10i(-10) + (-10i) + (10i) + (-10) = -10 - 10 - 10i + 10i
  5. Simplify expression: Simplify the expression by adding/subtracting the real parts and the imaginary parts.\newline−10−10+(−10i+10i)=−20+0i=−20-10 - 10 + (-10i + 10i) = -20 + 0i = -20

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