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For any complex number z prove that |R ...

For any complex number `z` prove that `|R e(z)|+|I m(z)|<=sqrt(2)|z|`

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RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. If z=x+i y , then show that z bar z +2(z+ bar z )+a=0 , where a in ...

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  2. If the real part of (z +2)/(z -1) is 4, then show that the locus of h...

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  3. For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

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  4. Find the square roots of the following: i

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  5. If ((1+i)/(1-i))^2=x+i y , findx+ydot

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  6. If for complex numbers z1 and z2 and |1-bar(z1)z2|^2-|z1-z2|^2=k(1-|z1...

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  7. If arg(z-1)=arg(z+2i), then find (x-1):y, where z=x+iy

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  8. Solve the equation |z|=z+1+2idot

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  9. If z 1 ​ and z 2 ​ are two non zero complex numbers such that ...

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

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

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

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

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

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

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

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

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

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

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

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