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Write the sum of the series i+i^2+i^3+.....

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

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RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

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

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

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

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

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

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

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

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  11. Find the real values of x and y for which (1+i)y^2+(6+i)=(2+i)x

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  12. Find the real values of xa n dy , if (3x-7)+2i y=-5y+(5+x)i

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  13. If (x+i y)^(1//3)=a+i b ,x ,y ,a b in Rdot Show that x/a+y/b=4(a^2-b^...

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  14. If a+i b=(c+i)/(c-i) , where c is real, prove that:a^2+b^2=1 and b/a=(...

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  15. Evaluate the following: i^(135)

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  16. Evaluate the following: i^(19)

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  17. Evaluate the following: i^(-999)

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  18. Evaluate the following: \ (-sqrt(-1))^(4n+3), ninNN

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  19. Evaluate the following: i^(457)

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  20. Evaluate the following: \ i^(528)

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