Math Forum :: View topic – two questions

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mathquark

Joined: 02 Oct 2004Posts: 16

Posted: Fri Jan 21, 2005 3:54 am    Post subject: two questions

1)x^a=2, x^(-b)=3 then find x^(a^2-b^2)=?

2)Let z be a complex number.If |z+(1/z)|=3 then find the minumum and maximum value of |z|

Kenny TM~

Frequent VisitorJoined: 20 Jan 2004Posts: 141

Posted: Fri Jan 21, 2005 11:37 am    Post subject: Re: two questions

mathquark wrote:

1)x^a=2, x^(-b)=3 then find x^(a^2-b^2)=?

2)Let z be a complex number.If |z+(1/z)|=3 then find the minumum and maximum value of |z|

1)

Andy

Frequent VisitorJoined: 28 Oct 2003Posts: 459

Location: Hong Kong

Posted: Sat Jan 22, 2005 5:58 pm    Post subject: Re: two questions

mathquark wrote:

2)Let z be a complex number.If |z+(1/z)|=3 then find the minumum and maximum value of |z|

If we write , then we have .

Therefore, we have . It gives .

In fact, if we set , the equality is achieved. Therefore, the maximum value of z is .

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