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With these kind of problems you are looking to find 2 values with which the output of the function is positive for one and negative for the other. In this scenario they have given 2 values 2 and 3 so the ...

rearrange gives z = [(1+2i)^2]/(2+i)expanding (1+2i)^2 gives 4i-3 therefore this becomes (4i-3)/2+i multiply that by the conjugate (2-i)/(2-i) to give (11i-2)/5therefore z= -2/5 + 11i/5

Markscheme:[M1] correct expansion shown, allowing sign slips.[A1] correct (unsimplified) expression obtained [A1] correct answer obtained (this can also earn both A1 marks if correct expression is not sho...