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Simplify the following expressions completely. a) 5(8+7i)5 ( 8 + 7 i ) Preview ​ b) (−7−4i)(3+2i)( - 7 - 4 i ) ( 3 + 2 i )

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Full solution

Q. Simplify the following expressions completely. a) 5(8+7i)5 ( 8 + 7 i ) Preview ​ b) (−7−4i)(3+2i)( - 7 - 4 i ) ( 3 + 2 i )
  1. Distribute 55: Distribute the 55 to both terms inside the parentheses for expression a)a).5×8+5×7i=40+35i5 \times 8 + 5 \times 7i = 40 + 35i
  2. Multiply using FOIL: Just multiply the numbers for expression b), using FOIL (First, Outer, Inner, Last).(−7)(3)+(−7)(2i)+(−4i)(3)+(−4i)(2i)=−21−14i−12i−8i2(-7)(3) + (-7)(2i) + (-4i)(3) + (-4i)(2i) = -21 - 14i - 12i - 8i^2
  3. Use i2=−1i^2 = -1: Remember that i2i^2 equals −1-1. So, −8i2-8i^2 becomes −8(−1)-8(-1) which is +8+8.
  4. Combine like terms: Combine like terms for expression b). \newline−21+8−14i−12i=−13−26i-21 + 8 - 14i - 12i = -13 - 26i

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