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If a+bi= ((x+i)^(2))/(2x^(2)+1), prove t...

If `a+bi= ((x+i)^(2))/(2x^(2)+1)`, prove that `a^(2) + b^(2)= ((x^(2) + 1)^(2))/((2x^(2) + 1)^(2))`

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ICSE-COMPLEX NUMBERS-Exercise (B)
  1. Perform the indicated operation and give your answer in the form x+yi,...

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  2. If x+ yi= (u+ vi)/(u-yi), prove that x^(2) + y^(2)=1

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  3. Prove that : [4 + 3 sqrt(-20)]^((1)/(2)) + [4 -3 sqrt(-20)]^((1)/(2))...

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  4. Express the following in the form a+ bi sqrt((5(2+i))/(2-i))

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  5. Express the following in the form a+ bi ((3-i)^(2))/(2+i)

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  6. Express the following in the form a+ bi (1+i)^(-3)

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  7. Express the following in the form a+ bi ((4i^(3)-i)^(2))/(2i+1)

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  8. Express the following in the form a+ bi (i-1)/(i+1)

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  9. Express the following in the form a+ bi (2+i)/((3-i)(1+2i))

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  10. Express the following in the form a+ bi (5)/(2i-7i^(2))

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  11. Prove that ((-1 + isqrt3)/(2))^(3) is a positive integer

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  12. If one of the values of x of the equation 2x^(2)-6x + k= 0 " be " (1)/...

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  13. Define conjugate complex numbers and show that their sum and product a...

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  14. If bar(z)= -z ne 0, show that z is necessarily a purely imaginary numb...

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  15. z and z' are complex numbers such that their product zz' = 3-4i. Given...

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  16. If a+bi= ((x+i)^(2))/(2x^(2)+1), prove that a^(2) + b^(2)= ((x^(2) + 1...

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  17. Let z(1)=2 -I, z(2)= -2 +i, find (i) Re ((z(1)z(2))/(bar(z)(1))), (ii)...

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  18. If z(1)= 3 + 5i and z(2)= 2- 3i, then verify that bar(((z(1))/(z(2))))...

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  19. If x= -2 - sqrt3i, where i= sqrt(-1, find the value of 2x^(4) + 5x^(3)...

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  20. If z= -3 + sqrt2i, then prove that z^(4) + 5z^(3) + 8z^(2) + 7z + 4 is...

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