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Question Number 558 by 112358 last updated on 26/Jan/15
Determinethecomplexnumberzsuchthatz2=tanx+icosx,intheformz=p+ik,p,k∈R.
Answered by prakash jain last updated on 26/Jan/15
(p+ik)2=tanx+icosx(p2−k2)+2ipk=tanx+icosxtanx=p2−k2⇒k2=p2−tanxcosx=2pkcos2x=4p2(p2−tanx)4p4−4p2tanx−cos2x=0p2=4tanx±16tan2x+16cos2x8p2=tanx+tan2x+cos2x2k2=p2−tanxk2=tan2x+cos2x−tanx2p=±tan2x+cos2+tanx2q=±tan2x+cos2x−tanx2Checkp2−q2=tanx2pq=2×±tan2x+cos2x+tanx2×±tan2x+cos2x+tanx2=(±×±)⋅2⋅tan2x+cos2x−tan2x4=cosx
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