Question 1117796
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Solve: |z| + z = 2 + i , where z is a complex no.
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Looking into equation, you can momentarily conclude that the imaginary part of z is i; in other words, 

z = a + i, where "a" is a real nnumber.


Then |z| = {{{sqrt(a^2 + 1)}}},  and the original equation implies for the real parts

{{{sqrt(a^2+1)}}} + a = 2,

{{{sqrt(a^2+1)}}} = 2 - a,   then squaring both sides

{{{a^2 + 1}}} = {{{4 - 4a + a^2}}},

1 = 4 - 4a,

4a = 4-1 = 3  ====>  a = {{{3/4}}}.


<U>Answer</U>.  z = {{{3/4 + i}}}.
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Solved.