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if cos (1-i) = a+ib, where a , b in R a...

if cos (1-i) = a+ib, where a , b `in ` R and `i = sqrt(-1)` , then

A

`a = (1)/(2)(e-(1)/(e))cos 1, b = (1)/(2)(e+(1)/(e))sin 1 `

B

`a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1`

C

`a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e+(1)/(e))sin 1`

D

`a=(1)/(2)(e-(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1`

Text Solution

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The correct Answer is:
B
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ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Single Option Correct Type Questions)
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  2. Number of roots of the equation z^10-z^5 -992=0 with negative real par...

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  3. If z1 and bar z1 represent adjacent vertices of a regular polygon of n...

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  4. If prod(p=1)^(r) e^(iptheta)=1, where prod denotes the continued produ...

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  5. If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0, where i=sqrt(-1), then z bar...

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  6. The centre of a square ABCD is at z=0, A is z(1). Then, the centroid o...

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  7. If z=(sqrt(3)-i)/2, where i=sqrt(-1), then (i^(101)+z^(101))^(103) equ...

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  8. Let alpha and beta be two fixed non-zero complex numbers and 'z' a var...

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  9. If alpha = cos((8pi)/11)+i sin ((8pi)/11) then Re(alpha + alpha^2+alph...

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  10. The set of points in an Argand diagram which satisfy both abs(z)le4 an...

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  11. If f(x)=g(x^(3))+xh(x^(3)) is divisiblel by x^(2)+x+1, then

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  12. If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...

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  13. Let C and R denote the set of all complex numbers and all real numb...

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  14. Let alpha and beta be two distinct complex numbers, such that abs(alph...

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  15. The complex number z satisfies thc condition |z-25/z|=24. The maximum ...

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  16. The points A,B and C represent the complex numbers z(1),z(2),(1-i)z(1)...

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  17. The system of equations |z+1-i|=sqrt2 and |z| = 3 has

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  18. Dividing f(z) by z-i, we obtain the remainder 1-i and dividing it by z...

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  19. The centre of circle represented by |z + 1| = 2 |z - 1| in the complex...

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  20. If x=9^(1/3) 9^(1/9) 9^(1/27) ......ad inf y= 4^(1/3) 4^(-1/9) 4^(1/...

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