InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Convert the complex number `(1+isqrt(3))` into polar form. |
|
Answer» The given complex number is `z = (1 + i sqrt(3))`. Let its polar form be `z = r(cos theta + i sin theta)`. Now, `r = |z| = sqrt(1^(2)(sqrt(3))^(2)) = sqrt(4) = 2`. Let `alpha` be the acute angle, given by `tan alpha = |(Im(z))/(Re(z))|=|(sqrt(3))/(1)|=sqrt(3) rArr alpha = (pi)/(3)`. Clearly, the point representing `z = (1 + i sqrt(3))` is P`(1, sqrt(3))`, which lies in the firest quadrant. `therefore" "arg(z) = theta = alpha = (pi)/(3)`. Thus, `r = |z| = 2 and theta arg(z) = (pi)/(3)`. Hence, the required polar form of `z = (1 + i sqrt(3))` is `2("cos"(pi)/(3) + "i sin"(pi)/(3))`. |
|