Given \(\displaystyle{\frac{{{z}_{{1}}}}{{{2}{z}_{{2}}}}}+{\frac{{{2}{z}_{{2}}}}{{{z}_{{1}}}}}={i}\) and 0, \(\displaystyle{z}_{{{1}}},{z}_{{{2}}}\) form

parksinta8rkv

parksinta8rkv

Answered question

2022-03-23

Given z12z2+2z2z1=i and 0, z1,z2 form two triangles with A,B the least angles of each. Find cotA+cotB.

Answer & Explanation

umgebautv6v2

umgebautv6v2

Beginner2022-03-24Added 10 answers

Write the equation z12z2+2z2z1=i as (z12z2)2iz12z2+1=0 and solve to obtain (z1z2)1,2=(5+1)eiπ2,>(51)ei3π2
Thus, the two are right triangles with |z1|>|z2| and
cotA+cotB=|(z2z1)1|+|(z2z1)2|=5+1+51=25

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