If a complex number Z with Im(Z)=4 satisfy ZZ+n=4i, where n is a positive integer, then the value of n is
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Solution
Let Z=x+iy
Given Im(Z)=4, then Z=x+4i
Now, ZZ+n=4i⇒x+4ix+4i+n=4i⇒x+4i=4i(x+4i+n)⇒x+4i=4ix−16+4in⇒x+4i=−16+4i(x+n)
Comparing the real and imaginary part, we get x=−16 and 4=4(x+n)∴n=17