# Polar coordinates of complex impedance

• joema
In summary, the question is asking for the impedance of a circuit in polar coordinates with an admittance of 7.09 millisiemens at 45 degrees. The official answer is 141 ohms at an angle of -45 degrees. However, there seems to be a discrepancy as the positive phase angle suggests inductance, not the given negative angle. Further clarification is needed to understand this.
joema
The question is: "In polar coordinates, what is the impedance of a circuit that has an admittance of 7.09 millisiemens at 45 degrees?"

The official answer is: "141 ohms at an angle of -45 degrees".

I don't understand this. 7.09 millisiemens is 141 ohms, and the positive phase angle indicates inductance, IOW a positive y value.

It seems the correct answer should be 141 ohms at an angle of 45 degrees, not -45 degrees.

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## 1. What are polar coordinates of complex impedance?

Polar coordinates of complex impedance refer to a way of representing a complex number in terms of its magnitude and angle. The magnitude is represented by the distance from the origin to the point on the complex plane, while the angle is the direction or phase of the complex number.

## 2. How are polar coordinates of complex impedance calculated?

To calculate the polar coordinates of complex impedance, we use the formula Z = R + jX, where R is the resistance component and X is the reactance component. Then, the magnitude can be calculated as |Z| = sqrt(R^2 + X^2) and the angle can be calculated as tan^-1(X/R).

## 3. What is the significance of using polar coordinates for complex impedance?

Using polar coordinates for complex impedance allows us to easily visualize and understand the magnitude and phase of a complex number. It also allows for simpler calculations when dealing with complex numbers in electrical circuits.

## 4. Can polar coordinates of complex impedance be converted to rectangular coordinates?

Yes, polar coordinates of complex impedance can be converted to rectangular coordinates using the formula Z = R + jX, where R is the magnitude and X is the angle. The rectangular coordinates are then given by Z = R(cosX + jsinX).

## 5. How are polar coordinates of complex impedance used in electrical engineering?

Polar coordinates of complex impedance are commonly used in electrical engineering to analyze and design circuits, as they provide a useful representation of complex numbers in circuits. They are also used in signal processing and communication systems.

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