I need helping with simplifying expression: \(\displaystyle{\frac{{{\left({1}+{i}\right)}^{{{33}}}}}{{{\left({1}-{i}\right)}^{{{33}}}}}}+{\left({1}-{i}\right)}^{{{10}}}+{\left({2}+{3}{i}\right)}{\left({2}-{3}{i}\right)}-{i}^{{-{7}}}\) What I

Oxinailelpels3t14

Oxinailelpels3t14

Answered question

2022-03-30

I need helping with simplifying expression:
(1+i)33(1i)33+(1i)10+(2+3i)(23i)i7
What I got is:
(1+i)33(1i)33+(1i)10+(2+3i)(23i)i7=(1+i)33(1i)33+(1i)10+13i7
My problems begin with
(1+i)33(1i)33
is it possible to simplify it without de Moivre or Euler's formulas?

Answer & Explanation

jmroberts70pbo2

jmroberts70pbo2

Beginner2022-03-31Added 10 answers

We can write
(1+i)33(1i)33=(1+i1i)33=(1+i1i1+i1+i)33=(2i2)33=i33=i
where the 3rd expression comes from rationalizing the denominator, multiplying by 1+i1+i

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