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If (pi)/(2) lt alpha (3pi)/(2) , the mod...

If `(pi)/(2) lt alpha (3pi)/(2) , the modulus argument form of `(1 + cos 2 alpha) + isin 2 alpha` is

A

`-2cos alpha{cos(alpha-pi)+isin(alpha-pi)}`

B

`2cos alpha{cos(alpha)+isinalpha)`

C

`2cos alpha{cos(-alpha)+isin(-alpha)}`

D

`-2cos alpha{cos(pi-alpha)+isin(pi-alpha)}`

Text Solution

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-COMPLEX NUMBERS -EXERCISE 1
  1. The mod -amplitude form of 1+cos theta-isin theta is

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  2. The mod -amplitude form of sintheta-i cos theta is

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  3. If (pi)/(2) lt alpha (3pi)/(2) , the modulus argument form of (1 + cos...

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  4. If (cos 3alpha+isin3alpha)(cos 5beta+isin5beta)=cos theta+isintheta " ...

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  5. If x+iy=cis, alpha, cis alpha then value of x^(2)+y^(2)

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  6. If cis alpha.cis beta.cis gamma=cis x then the value of x is

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  7. If A,B,C are angles of a triangle such that x = cis A , y = cis B , z...

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  8. For any two complex numbers z1,z2 and real numbers a and b , |az1 -bz2...

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  9. If |z1|=|z2|=1 , then |z1+z2| =

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  10. If (5z2)/(7z1) is purely imaginary , then |(2z1+3z2)/(2z1-3z2)|=

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  11. tan{ilog((a-ib)/(a+ib))}=

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  12. If |z-4//z|=2 then the greatest value of |z| is

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  13. The maximum value of |z| when z satisfies the condition |z+2/z|=2 is

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  14. The minimum value of |z-1|+ |z-5| is

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  15. If z(1) , z(2) are two complex numbers satisfying |(z(1) - 3z(2))/(3 -...

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  16. If the point z = (1+i) (1+2i)(1+3i)…(1+10i) lies on a circle with cent...

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  17. If |z-1| = 2 then the locus of z is

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  18. If |3z-2|=5 then the locus of z is

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  19. If |z-3+i| = 4 then the locus of z = x +iy is

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  20. If |(z-1)/(z-3)| = 2 then the locus of z = x +iy is

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