Question

Show that i+i30+i49+i61 is an imaginary number

Answer 1

Answer:

z=-1+3i

Step-by-step explanation:

Rectangular form:

z = -1+3i

Angle notation (phasor):

z = 3.1622777 ∠ 108°26'6″

Polar form:

z = 3.1622777 × (cos 108°26'6″ + i sin 108°26'6″)

Exponential form:

z = 3.1622777 × ei 1.8925469 = 3.1622777 × ei 0.6024164 π

Polar coordinates:

r = |z| = 3.1622777 ... magnitude (modulus, absolute value)

θ = arg z = 1.8925469 rad = 108.43495° = 108°26'6″ = 0.6024164π rad ... angle (argument or phase)

Cartesian coordinates:

Cartesian form of imaginary number: z = -1+3i

Real part: x = Re z = -1

Imaginary part: y = Im z = 3