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Let z1a n dz2 be two complex numbers suc...

Let `z_1a n dz_2` be two complex numbers such that `( z )_1+i( z )_2=0 and arg(z_1z_2)=pidot` Then, find `a r g(z_1)dot`

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RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. Find the number of solutions of z^2+|z|^2=0.

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  2. If ((a^2+1)/(2a-i))^2=x+i y , find the value of x^2+y^2dot

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  3. Let z1a n dz2 be two complex numbers such that ( z )1+i( z )2=0 and ...

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  4. If |z-5i|=|z+5i| , then the locus of zdot

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  5. If z1a n dz2 both satisfy z+barz r =2|z-1| and a r g(z1-z2)=pi/4 , t...

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  6. Show that the complex number z, satisfying the condition arg ((z -1)/(...

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  7. If z=(1+7i)/((2-i)^2) , then find |z|?

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  8. The value of (i^5+i^6+i^7+i^8+i^9)/(1+i) is

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  9. Write the least positive integral value of n for which ((1+i)/(1-i))^n...

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  10. If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is

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  11. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

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  12. What is the locus of z , if amplitude of (z-2-3i) is pi/4?

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  13. Write the sum of the series i+i^2+i^3+....... upto 1000 terms.

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  14. The sum and product of two complex numbers are real if and only if the...

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  15. If ((a+i)^2)/((2a-i))=p+i q , show that: p^2+q^2=((a^2+1)^2)/((4a^2+1)...

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  16. Write the value of a r g(z)+a r g(barz ) .

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  17. Express the following complex numbers in the standard form. Also find ...

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  18. Find the conjugate of 1/(3+4i)dot

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  19. If under root of (a+i b)/(c+i d)=x+i y , Prove (a^2+b^2)/(c^2+d^2)=(x...

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  20. Find real values of x and y for which the complex numbers -3+i x^2y ...

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