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+i sqrt(3))^(100), then [Re(z)/Im(z)] equals (a)2^(100)b.2^(50)c.(1)/(sqrt(3))dsqrt(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 z=(1+isqrt3)^100 , then frac{Re(z)}{Im(z)} equals

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=(-1)/(2)+i(sqrt(3))/(2) , then 8+10z+7z^(2) is equal to a) -(1)/(2)-i(sqrt(3))/(2) b) (1)/(2)+isqrt(3)/(2) c) -(1)/(2)+i(3sqrt(3))/(2) d) (sqrt(3))/(2)i

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