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If we express ((cos 2 theta-i sin 2 t...

If we express
`((cos 2 theta-i sin 2 theta)^(4)(cos 4 theta+i sin 4 theta)^(-5))/((cos 3 theta+i sin 3 theta)^(-2)(cos 3 theta-i sin 3 theta)^(-9))` in the form of `x+i y` we get

A

`cos 49 theta+i sin 49 theta`

B

`cos 21 theta+i sin 21 theta`

C

`cos 23 theta+i sin 23 theta`

D

`cos 49 theta-i sin 49 theta`

Text Solution

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The correct Answer is:
D
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
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  2. The modulus and amplitude of (1 + i)/(1-i) are

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  3. If we express ((cos 2 theta-i sin 2 theta)^(4)(cos 4 theta+i sin 4 ...

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  4. In the argand diagram the points representing the complex numbers 7 + ...

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  5. 1, omega, omega^(2) are cube roots of unit x, then their product is

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  6. The conjugate of ((2 + i)^(2))/(3+i) in the form of a + ib is

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  7. If z(2-i)=3+I,z^(20)=

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  8. Let z(1) and z(2) be n^(th ) roots of unity which subtend a right angl...

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  9. If omega=-(1)/(2)+i (sqrt(3))/(2), the value of [[1, omega, omega^(2)...

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  10. The amplitude of "sin"(pi)/(5)+i(1-"cos"(pi)/(5)) is

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  11. If sqrtx+(1)/(sqrt(x))=2costheta then x^(6)+x^(-6)=

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  12. Which of the following is a fourth root of

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  13. If omega=(-1+i sqrt(3))/(2) then (3+omega+3 omega^(2))^(4)=

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  14. If x+(1)/(x)=2cos alpha then x^(n)+(1)/(x^(n))=

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  15. The smallest positive integer for which(1 + i)^(2n)=(1 -l)^(2n) is

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  16. The real part of (1)/(1+cos theta+i sin theta) is

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  17. The modulus and amplitude of (1+2i)/(1-(1-i)^(2)) are respectively

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  18. The complex number ((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(...

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  19. If 2x=-1+sqrt(3)i, then the value of (1-x^(2)+x)^(6)-(1-x+x^(2))^(6)=

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  20. The modulus of amplitude of (1+i sqrt(3))^(8) are respectively

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