Question

3cis(5pi/4) in polar form

Answer 1

Rectangular form:
z = -2.1213203-2.1213203i

Angle notation (phasor):
z = 3 ∠ -135°

Polar form:
z = 3 × (cos (-135°) + i sin (-135°))

Exponential form:
z = 3 × ei (-0.75) = 3 × ei (-3π/4)

Polar coordinates:
r = |z| = 3 ... magnitude (modulus, absolute value)
θ = arg z = -2.3561945 rad = -135° = -0.75π = -3π/4 rad ... angle (argument or phase)

Cartesian coordinates:
Cartesian form of imaginary number: z = -2.1213203-2.1213203i
Real part: x = Re z = -2.121
Imaginary part: y = Im z = -2.12132034