Question

Convert the following into rectangular or cartesian form.
(i) 4 cis -330°
(ii) 10 cis 120°
(iii) 3 cis 0°
(iv) 4./2 cis – 45°​

Answer 1

Answer:

Rectangular form:

z = 3.5355339+3.5355339i

Angle notation (phasor):

z = 5 ∠ 45°

Polar form:

z = 5 × (cos 45° + i sin 45°)

Exponential form:

z = 5 × ei 0.7853982 = 5 × ei π/4

Polar coordinates:

r = |z| = 5 ... magnitude (modulus, absolute value)

θ = arg z = 0.7853982 rad = 45° = 0.25π = π/4 rad ... angle (argument or phase)

Cartesian coordinates:

Cartesian form of imaginary number: z = 3.5355339+3.5355339i

Real part: x = Re z = 3.536

Imaginary part: y = Im z = 3.53553391