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

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)