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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
- Find the reciprocal of : 7+ sqrt7 i.
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- Find the reciprocal of : i-5.
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- Find the complex number which when multiplied by 5 + 3i shall give 3 ...
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- Prove that : z= bar(z) iff z is real.
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- Prove that : z= -bar(z) iff z is either zero or purely imaginary.
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- Prove that: Re z= (z+bar(z))/2, Im z= (z-bar(z))/(2i).
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- Prove that : the sum of a complex number and its conjugate is real.
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- Prove that : the product of a complex number and its conjugate is real...
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- Give an example to show that subtraction of complex numbers is not com...
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- Find te sum and product of the complex numbers z1=-sqrt3+sqrt-2, z2=2s...
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- If z(1), z(2) are 1-i, -2 + 4i respectively, find I(m)((z(1)z(2))/(bar...
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- Find the values of x and y if : (x+iy)(1+i)=1-i where i=sqrt(-1)
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- Find the values of x and y if : ((1+i)x-2i)/(3+i)+((2-3i)y +i)/(3-i)...
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- If 1 +4 sqrt3i = (a+ ib)^2, prove that : a^2-b^2=1 and ab=2 sqrt3.
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- Show that if a, b,c, d in R, bar((a + ib) (c+ id)) = (a-ib)(c- id).
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- If x+iy=(a+ib)/(a-ib), then prove that x^2+y^2=1
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- If (a+i)^2/((2a-i))= p + iq, prove that : p^2+q^2 =(a^2+1)^2 /(4a^2+1)...
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- If x-iy= sqrt((a-ib)/(c-id)) prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d^...
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- If x-iy= sqrt((a-ib)/(c-id)), prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d...
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- If (x + iy)^3 = u + iv, then show that : u/x+v/y=4 (x^2-y^2).
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