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What is the smallest positive integer `n` for which `(1+i)^(2n)=(1-i)^(2n)?`

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RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. If z 1 ​ and z 2 ​ are two non zero complex numbers such that ...

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  2. If for complex numbers z1 and z2 ,arg(z1) - arg(z2)=0 , then show tha...

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  3. What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n...

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  4. If (1+i)z=(1-i) barz , then show that z=-i barz dot

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  5. Write the conjugate of (2-i)/((1-2i)^2) .

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  6. lf z(!=-1) is a complex number such that [z-1]/[z+1] is purely imagina...

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  7. If z and w are two complex number such that |zw|=1 and arg (z) – arg (...

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  8. The value of (1+i)^4+(1-i)^4 is

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  9. If the complex number z=x+i y satisfies the condition |z+1|=1, then ...

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  10. If z = x + iy lies in III quadrant, then bar z / z also lies in III qu...

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  11. If a=costheta+i sintheta, find the value of (1+a)/(1-a)dot

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  12. Let z1=r1(costheta1+isintheta1)a n dz2=r2(costheta2+isintheta2) be two...

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  13. For a positive integer n , find the value of (1-i)^n(1-1/i)^ndot

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  14. If (1+i)(1+2i)(1+3i)........(1+n i)=a+i b ,t h e n2xx5xx10 ....(1+n^2)...

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  15. Perform the indicated operation and find the result in the form a+i bd...

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  16. Let z1=2-i ,""""z2=-2+i . Find (i) Re ((z1z2)/( bar z1)) (ii) Im(1...

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  17. Which of the following is correct for any tow complex numbers z1a n dz...

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  18. If z1a n dz2 are two complex numbers such that |z1|=|z2|a n d arg(z1)...

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  19. Evaluate sum(n=1)^(13)(i^n+i^(n+1)), where n in Ndot

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  20. Evaluate 1+i^2+i^4+i^6+...+i^(2n)dot

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