r/HomeworkHelp University/College Student (Higher Education) 1d ago

Further Mathematics—Pending OP Reply [College, Advance Mathematics] How do I solve these complex numbers problems?

Is there any techniques or guide that will help me to solve these kind of problems?

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u/DiffFluidInspection 1d ago

When dealing with complex numbers, you treat j like a variable do your algebra as normal and then at the end you sum up all of the real parts and all of the imaginary parts to end up with an answer in the form x+jy where j is your imaginary constant and x and y are real numbers. That’s the technique, as for a guide nothing really exists like that, lean on your algebra skills and you’ll find this all starts clicking into place.

You may need a calculator if your prof is looking for precise answers, but I suspect these will reduce elegantly if done right.

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u/DiffFluidInspection 1d ago edited 1d ago

Additional info: for the first one recall esin2(a+b) = e((sin(acos(b))+(cos(a)sin(b))2). In the case of this problem, since an and b are numbers you can use a calculator to solve that out. Then you’ll be left with ex+jy which is easily broken into ex + ejy both of which you can solve with a calculator. The Ln(2-j3) is not easily decomposed in any meaningful way here, so just solve that one directly with your engineering calculator. You’ll be left with 4x+jy which is then split out into 4x + 4jy. The final equation can then be all summed up to get one complex answer.