Question

What are the values of magnitude ( r) and angle ( θ) for these complex numbers in polar form? a) (5 + 4)(4 +5j) and b) (5 +4j)/(4 +5) Write your answers here a) r b) r=

Answer 1

(a) r = 57.628

θ = 51.34°

(b) r = 0.711

θ = 38.65°

Explanation:

(a) Let's assume

z = (5 + 4)(4 +5j)

= 9 x (4+5j)

= 36 + 45j

magnitude of z can be given by

`\left | z \right |\ =\ r\ =√(36^2+45^2)`

=> r =57.628

angle of z can be given by,

`tan\theta\ =\ (45)/(36)`

`=>\ tan\theta=\ (5)/(4)`

`=>\ \theta\ =\ tan^(-1)(5)/(4)`

θ = 51.34°

(b) Let's assume

`z =\ ((5 +4j))/(5+4)`

`=\ ((5+4j))/(9)`

`=\ (5)/(9)+(4i)/(9)`

magnitude of z can be given by

`\left | z \right |=\ r=\sqrt{((5)/(9))^2+((4)/(9))^2}`

`=> r =(√(41))/(9)`

=> r = 0.711

angle of z can be given by,

`\ tan\theta\ =\ ((4)/(9))/((5)/(9))`

`=>\ tan\theta=\ (4)/(5)`

`=>\ \theta\ =\ tan^(-1)(4)/(5)`

=> θ = 38.65°