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KUMAR PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-MISCELLANEOUS EXERCISE :
- For any two complex numbers z(1) and z(2), prove that Re (z(1)z(2)) = ...
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- Reduce (1/(1-4i) -2/(1+i))((3-4i)/(5+i)) to the standard form.
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- If x-iy = sqrt((a+ib)/(c-id)), prove that (x^(2) + y^(2))^(2) = (a^(2)...
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- Conver the following in the polar form: (i) (1+7i)/(2-i)^(2), (ii) (...
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- Conver the following in the polar form: (i) (1+7i)/(2-i)^(2), (ii) (...
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- Solve: 3x^(2) - 4x + 20/3=0
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- x^(2)-2x + 3/2=0
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- 27x^(2) - 10x +1=0
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- 21x^(2) - 28x + 10=0
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- If z^(1) =2 -I, z(2)=1+i, find |(z(1) + z(2) + 1)/(z(1)-z(2) + 1)|
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- If a+ib = (x+i)^(2)/(2x^(2)+1), prove that a^(2) + b^(2) = (x^(2)+1)^(...
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- Let z(1) =2-I, z(2) =-2 + i, Find (i) (Re(z(1)z(2))/barz(1)), (ii) I...
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- Find the modulus and argument of the complex number (1+2i)/(1-3i)
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- Find the real numbers x and y if (x-iy) (3+5i) is the conjugate of -6 ...
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- Find the modulus of (1+i)/(1-i) - (1-i)/(1+i)
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- If (x+iy)^(3) = u + iy, then show that u/x + v/y = 4(x^(2)-y^(2))
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- If alpha and beta are different complex numbers with |beta|=1, then fi...
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- Find the numbers of non-zero integral solutions of the equation |1-i|^...
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- If (a+ib)(c+id)(e+if)(g+ih) = A + iB, then show that (a^(2) + b^(2))...
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- If ((1+i)/(1-i))^(m)=1, then find the least positive integral value of...
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