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24 February, 10:15

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

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  1. 24 February, 10:54
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    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)
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