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The smallest positive integer n for whi...

The smallest positive integer `n` for which `((1+i)/(1-i))^n=1` is (a)`8 `(b) `16 ` (c) `12 `(d) None of these

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To solve the problem, we need to find the smallest positive integer \( n \) such that \[ \left(\frac{1+i}{1-i}\right)^n = 1. \] ### Step 1: Simplify the expression ...
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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. The complex numbers z=x+iy which satisfy the equation |(z-5i)/(z+5i)|=...

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  2. Solve sqrt(5x^2-6x+8)-sqrt(5x^2-6x-7)=1.

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  3. The smallest positive integer n for which ((1+i)/(1-i))^n=1 is (a)8...

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  4. Solve sqrt(3x^2-7x-30)+sqrt(2x^2-7x-5)=x+5.

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  5. If the cube roots of unity are 1,omega,omega^2, then the roots of the ...

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  6. If x= (7+4sqrt(3)), prove that x+1//x= 14

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  7. Prove that the locus of midpoint of line segment intercepted between ...

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  8. Solve sqrt(5x^2-6x+8)-sqrt(5x^2-6x-7)=1.

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  9. Show that: sum(r=0)^(n-1)|z1+alpha^r z2|^2=n(|z1|^2+|z2|^2),w h e r e,...

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  10. Solve sqrt(x^2+4x-21)+sqrt(x^2-x-6)=sqrt(6x^2-5x-39.)

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  11. If alpha=(z-i)(z+i), show that, when z lies above the real axis, alpha...

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  12. Solve 4^x+6^x=9^xdot

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  13. Let x1, x2 are the roots of the quadratic equation x^2+a x+b=0,w h e r...

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  14. Solve 3^(2x^2-7x+7)=9.

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  15. Plot the region represented by pi/3lt=a r g((z+1)/(z-1))lt=(2pi)/3 in ...

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  16. How many solutions does the equation(8^x + 27^x)/(12^x +18^x) = 7/6hav...

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  17. Is the following computation correct? If not give the correct compu...

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  18. Consider an equilateral triangle having verticals at point A(2/sqrt3 e...

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  19. Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=...

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  20. Find the value of (i) (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(58...

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