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Assignment: Complex Numbers Date: 04thDec., 2009 Batch: X-1

1. If )(zf is a polynomial inzsuch that when it is divided by iz and iz+ , the emaindes ae espectivelyiandi +1 . Detemine the emainde when )(zf is divided by 1! +z .

!. "o any two comple# numbes !1 zandz , pove that

(i) !1!1!

!!

11!

!!

11 zzzzzzzzzz ++=++

(ii) !1!1!1!1!1 )(!

1)(

!

1zzzzzzzzzz ++++=+

$. "o comple# numbeszand w, pove that wzzwwz =!!

if and only if 1, == wzorwz

%. If &$