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If x+iy=(a+ib)/(a-ib), then prove that x...

If `x+iy=(a+ib)/(a-ib)`, then prove that `x^2+y^2=1`

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JBD PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-EXAMPLE
  1. Express the complex number given below in the form a + ib:- (-2-1/3i)^...

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  2. If x+iy=(a+ib)/(a-ib), then prove that x^2+y^2=1

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  3. Find the value of [i^19+(1/i)^25]^2

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  4. Express each of the complex number in the form of a+ib. (1/5+i2/5)

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  5. Express each of the complex number in the form of a+ib. (i-4)^2

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  6. If z=-3x+2yi and barz=6+4i, find the values of x and y.

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  7. z1=(3x+2y)+(x+2y)i is additive inverse of z2=5-i, find the values of x...

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  8. Write the following in the form a+ib 1/(3+4i)

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  9. Write the following in the form a+ib (1+i)^2/(3-i)

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  10. Find the multiplicative inverse of each of the following complex numbe...

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  11. Find the multiplicative inverse of each of the following complex numbe...

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  12. Find the multiplicative inverse of: z=cos theta- isintheta.

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  13. Verify that bar((2+3i)(1-2i))=bar((2+3i)) bar( (1-2i))

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  14. Find the modulus of the following complex numbers: (3-4i)/(4-31)

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  15. Find the modulus of the following complex numbers: (2+3i)^2/(1-3i)

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  16. Find the number of non-zero integral solutions of the equation |1- i|^...

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  17. If z=x+iy and |z+a|=3|z-a|, show that 2(x^2+y^2)=5ax-2a^2.

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  18. Solve 2x^2+x+1=0

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  19. Solve the following equation : 2x^2-(3 +7i)x + (9i-3)=0.

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  20. Find the modulus and argument of the complex number (1+2 i)/(1- 3i)

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