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If (x+i y)^(1//3)=a+i b ,\ then\ x/a+y/b...

If `(x+i y)^(1//3)=a+i b ,\ then\ x/a+y/b` is
a. `0` b. `1` c. `-1` d. none of these

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`(x+iy)^(1/3)=a+ib`
`(x+iy)=(a+ib)^3`
`=(a^3)+(ib)^3+3a^2(ib)+3a(ib)^2`
`a^3-ib^3+3ia^2b-3ab^2`
...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
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  2. If a=1+i , then a^2 equals A. 1-i B. 2i C. (1+i)(1-i) D. (i-1)

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  3. If (x+i y)^(1//3)=a+i b ,\ then\ x/a+y/b is a. 0 b. 1 c. -1 d. none o...

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  5. The argument of (1-isqrt(3))/(1+isqrt(3)) is a. 60^@ b. 120^@ c. 210^@...

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  7. If z=(1+2i)/(1-(1-i)^2), then arg(z) equals a. 0 b. pi/2 c. pi ...

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  10. If z=1-costheta+isintheta,\ t h e n\ |z| is a. 2sin(theta/2) b. 2cos(t...

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  11. If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is a. 0 b. 1 c. 100 d. n...

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  13. If x+i y=(3+5i)/(7-6i), then y is

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  14. The amplitude of 1/i is equal to-

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  15. The argument of (1-i)/(1+i) is-

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  16. The amplitude of (1+isqrt(3))/(sqrt(3)+i) is a. pi/3 b. -pi/3 c. pi/6 ...

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  17. (1+2i+3i^2)/(1-2i+3i^2) equals a. i b. -1 c. -i d. 4

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  18. The value of (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i^(580...

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  19. A real value of x satisfies the equation (3-4i x)/(3+4i x)=a-i b(a ,\ ...

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  20. The complex number which satisfies the condition |(i+z)/(i-z)|=1\ li...

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