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Question

If z=a+ib satisfy (4+2i)z+(82i)z=2+10i, where z is the complex conjugate of z, then the value of |a+2b| is

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Solution

Given : (4+2i)z+(82i)z=2+10i
z=a+ib,z=aib
Now,
(4+2i)z+(82i)z=2+10i4(z+2z)+2i(zz)=2+10i4(3aib)4b=2+10i(12a4b)i(4b)=2+10i12a4b=2,4b=10b=52, a=1|a+2b|=6

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