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(10-22 i)+(22 i)=
Express your answer in the form 
(a+bi).

(1022i)+(22i)= (10-22 i)+(22 i)= \newlineExpress your answer in the form (a+bi) (a+b i) .

Full solution

Q. (1022i)+(22i)= (10-22 i)+(22 i)= \newlineExpress your answer in the form (a+bi) (a+b i) .
  1. Identify complex numbers: Identify the real and imaginary parts of the complex numbers.\newlineThe real part of the first complex number is 1010, and the imaginary part is 22i-22i. The second complex number has no real part and an imaginary part of 22i22i.
  2. Add real parts: Add the real parts together.\newlineSince the second complex number has no real part, the real part of the sum is just the real part of the first complex number, which is 1010.
  3. Add imaginary parts: Add the imaginary parts together.\newlineThe imaginary parts are 22i-22i and 22i22i. When we add them together, they cancel each other out because 22i+22i-22i + 22i equals 0i0i.
  4. Combine real and imaginary parts: Combine the sum of the real parts and the sum of the imaginary parts.\newlineThe sum of the real parts is 1010, and the sum of the imaginary parts is 0i0i. Therefore, the sum of the two complex numbers is 10+0i10 + 0i.
  5. Express answer in (a+bi)(a+bi) form: Express the answer in the form (a+bi)(a+bi).\newlineSince the imaginary part is 00, the expression simplifies to just the real part, which is 1010. So the answer in the form (a+bi)(a+bi) is 10+0i10 + 0i, which can be written simply as 1010.

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