Question

Two complex numbers are given byz1= 3 +j4 andz2= 2 +j3. Determine in both polar andCartesian forms

Answer 1

Answer:

Cartesian

z₁= 3 +4*j

z₂= 2 +3*j

Polar

z₁=5 * e^ (0.927*j)

z₁=√13 * e^ (0.982*j)

Step-by-step explanation:

for the complex numbers z the cartesian form of is

z= x + y*j

then

1) z₁= 3 +4*j (cartesian form)

2) z₂= 2 +3*j (cartesian form)

the polar form is

z= r* e^jθ

where

r= √(x²+y²) → r₁ = √(3²+4²) = 5 ,  r₂ = √(2²+3²) = √13

and

θ = tan⁻¹ (y/x)  → θ₁  = tan⁻¹ (4/3)= 0.927 rad , θ₂  = tan⁻¹ (3/2)= 0.982 rad

then

z₁=5 * e^ (0.927*j)

z₁=√13 * e^ (0.982*j)