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)`

If z=(-1)/(2)+i(sqrt(3))/(2), " then "8+10z+7z^(2) is equal to

The value of ((-1 + isqrt3)/(2))^(100) + ((-1-isqrt3)/(2))^(100) is :

If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)dot

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

If |z-3|=min{|z-1|,|z-5|} , then Re(z) equals to

If |z-(1/z)|=1, then (|z|)_(m a x)=(1+sqrt(5))/2 b. (|z|)_(m in)=(sqrt(5)-1)/2 c. (|z|)_(m a x)=(sqrt(5)-2)/2 d. (|z|)_(m in)=(sqrt(5)-1)/(sqrt(2))

Let L be the line of intersection of the planes 2x+3y+z=1a n dx+3y+2z=2. If L makes an angle alpha with the positive x-axis, then cosalpha equals a. 1/2 b. 1 c. 1/(sqrt(2)) d. 1/(sqrt(3))

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