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Find the sum of 9+9i9 + 9i and its complex conjugate.\newlineWrite your answer in the form a+bia + bi.

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Full solution

Q. Find the sum of 9+9i9 + 9i and its complex conjugate.\newlineWrite your answer in the form a+bia + bi.
  1. Reasoning: Identify conjugate: Reasoning: Identify the complex conjugate of 9+9i9 + 9i. Calculation: The complex conjugate of 9+9i9 + 9i is 9−9i9 - 9i. Math Error Check:
  2. Calculation: Complex conjugate: Reasoning: Add the original complex number and its conjugate. Calculation: (9+9i)+(9−9i)(9 + 9i) + (9 - 9i) Math Error Check:
  3. Math Error Check: Reasoning: Combine like terms. Calculation: 9+9−9i+9i9 + 9 - 9i + 9i Math Error Check:
  4. Reasoning: Add conjugate: Reasoning: Simplify the expression.\newlineCalculation: 9+9=189 + 9 = 18 and −9i+9i=0-9i + 9i = 0\newlineMath Error Check:
  5. Calculation: Add numbers: Reasoning: Write the final answer in the form a+bia + bi. Calculation: 18+0i=1818 + 0i = 18 Math Error Check:

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