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Convert the complex number z=(i-1)/(cosp...

Convert the complex number `z=(i-1)/(cospi/3+isinpi/3)`in the polar form.

A

`r = sqrt(2) [ cos "" ( 5 pi)/( 12) + i sin "" ( 5 pi)/( 12)]`

B

` r = sqrt(2) ( cos "" (pi)/( 4) + isin "" (pi)/(4))`

C

`r = sqrt(2) ( cos "" (pi)/(6) + isin "" (pi)/( 6))`

D

none of these

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The correct Answer is:
A
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ML KHANNA-COMPLEX NUMBERS -Self Assessment Test
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  2. If one root of the equation x^2 + (1 - 3i) x - 2(1+i) = 0 is -1 +i, th...

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  3. Convert the complex number z=(i-1)/(cospi/3+isinpi/3)in the polar form...

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  4. If z(1) , z(2), z(3) are three complex numbers in A.P., then they lie ...

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  5. The complex number(1+2i)/( 1-i) lies in the Quadrant number

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  6. If xr=cos(pi/(2^r))+isin(pi/(2^r)) then x1,x2,x3,.....oo

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  7. If p(x,y) denotes z = x + iy in Argand plane and | (z - 1)/( z + 2i)|...

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  8. If omega (!= 1) is a cube root of unity, then the sum of the series S ...

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  9. The smallest positive integral value of 'n' such that [(1+sin\ pi/8 + ...

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  10. If 1 , omega and omega^(2) are the cube roots of unity, then the valu...

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  11. If Z=ilog(2-sqrt(3)),then cos(Z)=

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  12. If z = |{:(1 , 1 + 2i, - 5i),(1 - 2i,-3,5+3i),(5i,5-3i,7):}|, then (i=...

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  13. sum(k=1)^6 (sin,(2pik)/7 -icos, (2pik)/7)=?

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  14. Let z be a complex number such that the imaginary part of z is nonzero...

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  15. If z ne 1 and (z^(2))/(z-1) is real, the point represented by the comp...

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  16. If omega(ne 1) be a cube root of unity and (1+omega)^(7)=A+Bomega, the...

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  17. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

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  18. If z is any complex number satisfying | z - 3- 2i | le 1 then the min...

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  19. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

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  20. If z is a complex number of unit modulus and argument theta then arg...

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