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Find the least positive integer 'n' such...

Find the least positive integer 'n' such that `((1+i)/(1-i))^(n) =1`.

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The correct Answer is:
n=4
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SUBHASH PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -THREE MARKS QUESTIONS WITH ANSWERS
  1. Find the least positive integer 'n' such that ((1+i)/(1-i))^(n) =1.

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  2. Find the square roots of the following: (i) -15-8i

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  3. Find the square roots of the following: (i) -15-8i

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  4. Find the square roots of the following: (i) -15-8i

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  5. Reduce (1/(1-4i) -2/(1+i))((3-4i)/(5+i)) to the standard form.

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  6. (i) If x-iy = sqrt((a-ib)/(c-id)) prove that (x^(2) + y^(2)) =(a^(2) +...

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

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  8. (iii) Find the modulus and argument of the complex numbers. (a) (1+i...

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  9. Convert the following in the polar form: (i) (1+7i)/(2-i)^(2) (ii)...

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

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  11. Find real theta such that (3 + 2i sin theta)/(1-2i sin theta) is purel...

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  12. Convert the complex number z=(i-1)/(cos pi/3 + isinpi/3) in the polar ...

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  13. If ((1+i)/(1-i))^(2m)=1, then find the least integral value of m.

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  14. Solve each of the following equations. 1. Solve x^(2) +x+1=0

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  15. x^(2) + x + 1/sqrt(2)=0

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  16. Solve: 2x^(2) + x+1=0

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  17. Solve x^(2) + 3x + 5=0

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  18. Solve x^(2)-x +2=0

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  19. x^(2) + x + 1/sqrt(2)=0

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  20. Solve sqrt(5)x^(2) + x + sqrt(5)=0

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  21. Find the square roots of the following: (i) -15-8i

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