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Z = xyi =⇒ z = x−iy The "bar" operation is pretty nice It is called complex conjugation Consider the following example z = 2 3i and w = 4 5i Then z = 2 − 3i and Problem Prove that this always works So, take z = abi and w = cdi and calculate the whole thing outZ = X −Y W = X Solve it with respect to the original random variables and get (X = W Y = W − Z For the last system the Jacobian is J = 0 1 −1 1 # c) Find the pdf of Z = X/Y Let us check Method A Write Introduce a new pair of onetoone RVs (Z = X/Y W = X Solve it with respect to the old variables (Y = W/ZX o v W } i o À Ç X W Z v P W & } µ W } v o µ } v í í X ^ µ u u Ç v v Æ v o Ç î ì í õ U W Z P Ì Á Z v µ Ç Æ } À o } ( } Z P v v 1 ƒXƒ}ƒz ƒWƒ‡ƒWƒ‡ ƒŠƒIƒ" •ÇŽ†