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)`

Write the comple number in a + ib form unsing cube roots of unity: (a) (-(1)/(2) + sqrt(3)/(2)i)^(1000) (b)If z =(sqrt(3) + i)^(17)/((1-i)^(50)) (c) (i + sqrt(3))^(100) + (i+ sqrt(3))^(100) + 2^(100)

If z = (sqrt(2) - sqrt(-3)) , find Re(z), Im(z), bar(z) and |z| .

If z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Im (z) equals to

If z_(1)=1+sqrt(3)i,z_(2)=1-sqrt(3)i, then (z_(1)^(100)+z_(2)^(100))/(z_(1)+z_(2))=

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

If |z-1|=|z-5| and |z|=sqrt13 ,then find |Im(z)|

If z=(1)/(2)(i sqrt(3)-1), then find the value of (z-z^(2)+2z^(3))(2-z+z^(2))

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=,z_3=1-isqrt(3)