Given `z=(1+isqrt(3))^(100),` then `[Re(z)//Im(z)]` equals (a)`2^(100)` b. `2^(50)` c. `1/(sqrt(3))` d. `sqrt(3)`

Given z=(1+isqrt(3))^(100), then [R E(z)//I M(z)] equals 2^(100) b. 2^(50) c. 1/(sqrt(3)) d. sqrt(3)

If arg ((z_(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z_(1)|=3 , then |z_(1)| equals to a. sqrt(3) b. 2sqrt(2) c. sqrt(10) d. sqrt(26)

If z is a complex number such that |z|=4 and a r g(z)=(5pi)/6 , then z is equal to -2sqrt(3)+2i b. 2sqrt(3)+i c. 2sqrt(3)-2i d. -sqrt(3)+i

If z is a complex number such that |z|=4 and a r g(z)=(5pi)/6 , then z is equal to -2sqrt(3)+2i b. 2sqrt(3)+i c. 2sqrt(3)-2i d. -sqrt(3)+i

The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4 is a. sqrt(30) b. 2sqrt(30) c. 5sqrt(30) d. 3sqrt(30)

The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4 is a. sqrt(30) b. 2sqrt(30) c. 5sqrt(30) d. 3sqrt(30)

If the complex number z_1,z_2 and z_3 represent the vertices of an equilateral triangle inscribed in the circle |z|=2 and z_1=1+isqrt(3) then (A) z_2=1,z_3=1-isqrt(3) (B) z_2=1-isqrt(3),z_3=-isqrt(3) (C) z_2=1-isqrt(3), z_3=-1+isqrt(3) (D) z_2=-2,z_3=1-isqrt(3)

If z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5 , then prove that Im(z)=0

If z=(sqrt(3)-i)/2 , where i=sqrt(-1) , then (i^(101)+z^(101))^(103) equals to

Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-2)/1=(y-3)/1=(z-4)/1 is equal to a. sqrt(14) b. sqrt(7) c. sqrt(2) d. none of these