express z =√3 + 1j in polar form with the argument in degrees?

Answer 1

First find the length of the of z. Call the length L.

L^2 = (sqrt(3))^2 + 1^2
L^2 = 3 + 1 = 4

L = 2.

Now find the angle that x makes with the x axis. Call the angle t

tan(t) = 1/sqrt(3)
t = 30 degrees.

So in polar form, z = 2(angle sign)30 degrees

Answer 2

In the complex plane we may take the argument as the arctangent value of (1/V3), that is 30 degrees.
The modulus is V(3 + 1) = 2
then
z = 2 (cos 30 + i sin 30)

i has been used instead of j

Answer 3

z = x + iy Polar variety: z = r(cos ? + i sin ?) the position r = |z| = ?(x² + y²) ? = arg z = tan?¹ (y/x) Coordinates of z on a Cartesian airplane determines ?: ? = tan?¹ (y/x) . . . . . . . [even as z is contained in the first quadrant, z(x, y)] ? = ? – tan?¹ (y/x) . . . . [even as z is contained in the 2d quadrant, z(-x, y)] ? = ? + tan?¹ (y/x) . . . . [even as z is contained in the third quadrant, z(-x, -y)] ? = -tan?¹ (y/x) . . . . . . .[even as z is contained in the 4th quadrant, z(x, -y)] For this situation, z = ?3 – i r = ?[(?3)² + (-a million)²] . = ?[3 + a million] . = ?4 . = 2 on the Cartesian airplane, z(?3, -a million) lies on 4th quadrant, ? = -tan?¹ (y/x) . = -tan?¹ (a million/?3) . = -?/6 (-30° or 330°) Polar variety: z = 2[cos (-?/6) + i sin (-?/6)] . .= 2[cos (11?/6) – i sin (11?/6)] In degrees: z = 2[cos (-30°) + i sin (-30°)] . .= 2[cos 330° – i sin 330°] wish you comprehend.