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Multiply and simplify the following complex numbers: (2+5i)*(5-3i)

Multiply and simplify the following complex numbers:\newline(2+5i)⋅(5−3i) (2+5 i) \cdot(5-3 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+5i)⋅(5−3i) (2+5 i) \cdot(5-3 i)
  1. Distribute Terms: Distribute each term in the first complex number by each term in the second complex number.\newline(2+5i)⋅(5−3i)=2⋅5+2⋅(−3i)+5i⋅5+5i⋅(−3i)(2+5i)\cdot(5-3i) = 2\cdot 5 + 2\cdot(-3i) + 5i\cdot 5 + 5i\cdot(-3i)
  2. Perform Multiplication: Perform the multiplication for each term.\newline2×5=102 \times 5 = 10\newline2×(−3i)=−6i2 \times (-3i) = -6i\newline5i×5=25i5i \times 5 = 25i\newline5i×(−3i)=−15i25i \times (-3i) = -15i^2
  3. Simplify i2i^2: Remember that i2=−1i^2 = -1 and simplify the expression.\newline−15i2=−15∗(−1)=15-15i^2 = -15*(-1) = 15
  4. Combine Like Terms: Combine like terms.\newline10−6i+25i+1510 - 6i + 25i + 15\newline10+15=2510 + 15 = 25\newline−6i+25i=19i-6i + 25i = 19i
  5. Final Answer: Add the real parts and the imaginary parts together to get the final answer. 25+19i25 + 19i

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