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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
- Find the range of real number alpha for which the equation z+alpha|z-1...
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- If a, b are real, prove that the equation z^2+az+b=0 will not have any...
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- Find the maximum and minimum values of |z| satisfying |z+(1)/(z)|=2
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- If |z|ge3, then determine the least value of |z+(1)/(z)|.
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- If z is a complex number such that |z+1/z|=1 show that Re(z)=0 when |z...
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- Locate the region in the Argand plane for the complex number z satisfy...
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- Indicate the region represented by pi/6leargzlepi/4 .
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- Indicate the region in the Argand plane respresented by |z+1|^2+|z-1|^...
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- Prove that the product of any number of unimodular complex numbers is ...
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- Separate the real and imaginary parts of frac((cosalpha+isinalpha)(cos...
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- Prove that (frac(1+costheta+isintheta)(1+costheta-isintheta))^n=cos nt...
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- If alpha=pi/12 ,prove that frac((cosalpha+isinalpha)(cos2alpha+isin2al...
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- Prove that (frac(cosx+isinx)(sinx+icosx))^5=cos(10x-frac(5pi)(2))+isin...
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- Find the value of : root(4)(1).
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- Find the value of : 1^(1//5).
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- Find the value of : (1-i)^(1//3).
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- Find the value of : (1-sqrt3i)^(2//5).
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- Find the value of : root(4)(-64).
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- Find the value of : (1+i)^n, n inN
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- Solve for x : x^5-1=0.
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