Exponential to Rectangular and Polar Form Conversion Convert the complex number Z1 = 2.828e^j45° from exponential form to rectangular form and polar forms.

Question

Exponential to Rectangular and Polar Form Conversion

Convert the complex number [latex]Z_1=2.828 e^{j 45^{\circ}}[/latex] from exponential form to rectangular form and polar forms.

Accepted Answer

The polar form for [latex]Z_1=2.828 e^{j 45^{\circ}}[/latex] is:

[latex]Z_1=2.828 \angle 45^{\circ}[/latex]

Using Equation (C.1):

[latex]\begin{aligned}&\left\{\begin{array}{l}r=\sqrt{a^2+b^2} \ heta= an ^{-1} \frac{b}{a}\end{array} ight. \&\left\{\begin{array}{l}a=r \cdot \cos heta \b=r \cdot \sin heta\end{array} ight.\end{aligned}[/latex] (C.1)

a = r cosθ = 2.828 × cos(45°) = 2

b = r sinθ = 2.828 × sin (45°) = 2

Therefore, the rectangular form is:

[latex]Z_1=a+j b=2+j 2[/latex]

Question C.3: Exponential to Rectangular and Polar Form Conversion Convert...

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