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If (a+i)^2/(2a-i) = p+iq, prove that p^2...

If `(a+i)^2/(2a-i) = p+iq`, prove that `p^2+q^2 = (a+1)^2/(4a^2+1)`

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A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Match the following

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  2. If x = 4 + sqrt7i, find x^2 and x^3.Hence, find the value of x^3-4x^2-...

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  3. If (a+i)^2/(2a-i) = p+iq, prove that p^2+q^2 = (a+1)^2/(4a^2+1)

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  4. Sheeba proved the same relation stated above by expressing (a+i)^2/(2a...

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  5. Match the following

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  6. Suppose z1 = 2(cos60^@ + isin60^@) and z2 = 4(cos30^@ + isin30^@) Find...

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  7. Suppose z1 = 2(cos60^@ + isin60^@) and z2 = 4(cos30^@ + isin30^@) find...

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  8. Suppose z1 = 2(cos60^@ + isin60^@) and z2 = 4(cos30^@ + isin30^@) Find...

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  9. Express (1-3i)/(1+2i) in the form x+iy

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  10. Find the polar form of the complex number (1-3i)/(1+2i)

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  11. Convert the following complex numbers into polar form 1 - i

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  12. Represent the complex number sqrt3+i in the polar form.

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  13. Express (1-i)/(sqrt3+i) in polar form

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  14. Express (1-i)(sqrt3+i) in polar form

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  15. Plot the points represented by the complex numbers 1+i, 2+i, 2+3i, 1+3...

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  16. What are the cartesian co-ordinates of the points 1+i, 2+i, 2+3i, 1+3...

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  17. If two points P and Q are represented by the complex numbers z1 and z2...

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  18. If the points P,Q,R,S are representing the complex numbers -1, 3i, 3+2...

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  19. If z = x+iy, prove that arg(z -1) = tan^(-1)(y/(x-1)) and arg(z+1) = t...

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  20. If arg((z-1)/(z+1)) = pi/2, show that x^2+y^2-1=0

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