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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
- Find all non zero complex numbers z satisfying barz=iz^2
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- Express (2+i)^2/(2+3i) in the form x+iy.
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- if z=(3-4i)/((4-2i)(1+i) then find Re(z).
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- IF frac(sinfrac(x)(2)+cosfrac(x)(2)+itanfrac(x)(2))(1+2isinfrac(x)(2) ...
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- Simplify 20/(sqrt3-sqrt(-2))+30/(3sqrt(-2)-2sqrt3)-14/(2sqrt3-sqrt(-2)...
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- Find all values of theta for which (1-isintheta)/(1+icostheta) is pur...
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- Find the real values of x\ a n d\ y ,\ if:(3m-2i)(2+i)^2=10(1+i)
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- (x+i y)(2-3i)=4+i
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- Find all complex numbers z for which (z-2)/(z+2) is purely imaginary.
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- Find the real value of x and y if ((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)...
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- If z1=-3+ixy,z2=x+y+4i and z1=barz2 then find x and y .
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- Evaluate: [i^19+(1/i)^25]^2
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- Evaluate (i^17-1/i^34)^3 .
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- If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...
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- Prove that (1+i)^(2n)+(1-i)^(2n)= 0 if n is an odd integer and, equal ...
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- If x=sqrt(-2)-1 find he value of x^4+4x^3+6x^2+4x+9
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- If a=(1+i)/sqrt(2) find the value of a^6+a^4+a^2+1
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- If sqrt(a-ib)= x-iy , prove that sqrt(a+ib)=x+iy.
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- If root(3)(a+ib) = x + iy, prove that : root(3)(a-ib) = x- iy .
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- (x+iy)^(1/3) =(a+ib) then prove that (x/a+y/b)=4(a^2-b^2)
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- Express (1+a^2)(1+b^2) as the sum of two squares.
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