Q. (8−10i)−(−16+2i)=Express your answer in the form (a+bi).
Identify numbers to subtract: Identify the numbers to be subtracted.We have two complex numbers: (8−10i) and (−16+2i). We need to subtract the second complex number from the first one.
Change subtraction to addition: Change the subtraction to addition by distributing the negative sign to the second complex number.(8−10i)−(−16+2i) becomes (8−10i)+(16−2i) when we distribute the negative sign.
Combine real parts: Combine the real parts of the complex numbers.The real part of the first complex number is 8, and the real part of the second complex number is 16. Adding these together gives us 8+16.
Calculate sum of real parts: Calculate the sum of the real parts. 8+16=24.
Combine imaginary parts: Combine the imaginary parts of the complex numbers.The imaginary part of the first complex number is −10i, and the imaginary part of the second complex number is −2i. Adding these together gives us −10i−2i.
Calculate sum of imaginary parts: Calculate the sum of the imaginary parts. −10i−2i equals −12i.
Combine results in (a+bi) form: Combine the results of the real and imaginary parts to express the answer in the form (a+bi).The real part is 24 and the imaginary part is −12i, so the final answer is 24−12i.
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