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(-3+71 i)+(9)=
Express your answer in the form 
(a+bi).

(3+71i)+(9)= (-3+71 i)+(9)= \newlineExpress your answer in the form (a+bi) (a+b i) .

Full solution

Q. (3+71i)+(9)= (-3+71 i)+(9)= \newlineExpress your answer in the form (a+bi) (a+b i) .
  1. Identify numbers to be added: Identify the numbers to be added.\newlineWe have two numbers: a complex number (3+71i)(-3+71i) and a real number 99. The real number can be thought of as a complex number with an imaginary part of 00, so it is 9+0i9 + 0i.
  2. Add real parts of complex numbers: Add the real parts of the complex numbers.\newlineThe real part of (3+71i)(-3+71i) is 3-3, and the real part of 9+0i9 + 0i is 99. Adding these together gives us 3+9-3 + 9.
  3. Perform addition of real parts: Perform the addition of the real parts.\newlineCalculating 3+9-3 + 9 gives us 66.
  4. Add imaginary parts of complex numbers: Add the imaginary parts of the complex numbers.\newlineThe imaginary part of (3+71i)(-3+71i) is 71i71i, and the imaginary part of 9+0i9 + 0i is 0i0i. Adding these together gives us 71i+0i71i + 0i.
  5. Perform addition of imaginary parts: Perform the addition of the imaginary parts.\newlineCalculating 71i+0i71i + 0i gives us 71i71i.
  6. Combine real and imaginary parts: Combine the results of the real and imaginary parts.\newlineWe combine the real part 66 and the imaginary part 71i71i to express the sum in the form (a+bi)(a+bi).
  7. Write final answer: Write the final answer.\newlineThe sum of (3+71i)(-3+71i) and 99 is 6+71i6 + 71i.

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