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((-21+65 i)+(-30+12 i)=)/({:[-×],[+=]:}) Express your answer in the form (a+bi).

(−21+65i)+(−30+12i)=−×+≠ \frac{(-21+65 i)+(-30+12 i)=}{\substack{-\times \\+\neq}} \newlineExpress your answer in the form (a+bi) (a+b i) .

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Q. (−21+65i)+(−30+12i)=−×+≠ \frac{(-21+65 i)+(-30+12 i)=}{\substack{-\times \\+\neq}} \newlineExpress your answer in the form (a+bi) (a+b i) .
  1. Addition of Real Parts: To add two complex numbers, we add their real parts together and their imaginary parts together separately.\newlineSo, we take the real part of the first complex number, −21-21, and add it to the real part of the second complex number, −30-30.\newline−21+(−30)=−51-21 + (-30) = -51
  2. Addition of Imaginary Parts: Next, we add the imaginary parts together. We take the imaginary part of the first complex number, 65i65i, and add it to the imaginary part of the second complex number, 12i12i.\newline65i+12i=77i65i + 12i = 77i
  3. Combining the Real and Imaginary Parts: Now we combine the sum of the real parts with the sum of the imaginary parts to get the final result in the form (a+bi)(a+bi).\newlineThe sum is −51-51 for the real part and 77i77i for the imaginary part.\newlineSo, the sum of the two complex numbers is (−51+77i)(-51 + 77i).

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