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If (1+i)(1+2i)(1+3i)…(1+ni)=x+iy, show t...

If `(1+i)(1+2i)(1+3i)…(1+ni)=x+iy`, show that 2.5.10…`(1+n^2) = x^2+y^2`

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A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. If (costheta-isintheta)^2 = x -iy, show that x^2+y^2 = 1

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  2. Find the modulus of the complex number ((1+i)(2+i))/(3+i)

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  3. If (1+i)(1+2i)(1+3i)…(1+ni)=x+iy, show that 2.5.10…(1+n^2) = x^2+y^2

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  4. Express the following complex numbers in a+ib form. (a) (5i)(-(3)/5i)

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  5. Express the following complex numbers in a+ib form. (b) i^9+i^(19)

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  6. Express the following complex numbers in a+ib form. (c ) i^(-39)

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  7. Express the following in a+ib form 3(7+7i)+i(7+7i)

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  8. Express the following in a+ib form (1-i)-(-1+6i)

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  9. Express the following in a+ib form (1/5+i2/5)-(4+5/2i)

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  10. Express the following in a+ib form. [(1/3+i7/3)+(4+i1/3)]-[-4/3+i]

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  11. Express the following in a+ib form. (1-i)^4

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  12. Express the following in a+ib form (1/3+3i)^3

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

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  14. Find the multiplicative inverse of the following complex number 4-3i

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  15. Find the multiplicative inverse of the following, sqrt5+3i

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  16. Find the multiplicative inverse of the following complex number -i

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  17. Express the following expression in the form a+ib ((3+isqrt5) (3-isqrt...

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  18. Write the values of i^2, i^4 and i^6

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  19. Show that 1+i^2+i^4+i^6=0

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  20. Using the value of i^2, prove that 1/i=-i

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