If the rectangular form of a complex number is A+ jB, where A and B are positive, what is the polar form of the complex number? O VA + B)² Ztan (4) O VA? + B? tan(4) O (A² + B²)Z tan 1(4) O VA? + B? L tan 1(4)
If the rectangular form of a complex number is A+ jB, where A and B are positive, what is the polar form of the complex number? O VA + B)² Ztan (4) O VA? + B? tan(4) O (A² + B²)Z tan 1(4) O VA? + B? L tan 1(4)
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![### Converting Complex Numbers from Rectangular to Polar Form
If the rectangular form of a complex number is \(A + jB\), where \(A\) and \(B\) are positive, what is the polar form of the complex number?
### Options for Polar Form
1. \[
\sqrt{(A + B)^2} \angle \tan^{-1} \left(\frac{B}{A}\right)
\]
2. \[
\sqrt{A^2 + B^2} \angle \tan^{-1} \left(\frac{A}{B}\right)
\]
3. \[
(A^2 + B^2) \angle \tan^{-1} \left(\frac{B}{A}\right)
\]
4. \[
\sqrt{A^2 + B^2} \angle \tan^{-1} \left(\frac{B}{A}\right)
\]
### Explanation:
To convert from rectangular form to polar form, use the following:
- Magnitude: \( r = \sqrt{A^2 + B^2} \)
- Angle (in radians): \( \theta = \tan^{-1}\left(\frac{B}{A}\right) \)
In polar form, the complex number is expressed as \( r \angle \theta \).
### Correct Choice:
The correct polar form is:
\[
\sqrt{A^2 + B^2} \angle \tan^{-1} \left(\frac{B}{A}\right)
\]
This formula represents the magnitude and angle of the complex number in polar coordinates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd65464ea-20ac-437a-9b4f-902b3affc00d%2F0721cf02-8be8-4e6a-b23d-f3dfecd7bd05%2Fqb6s1oo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Converting Complex Numbers from Rectangular to Polar Form
If the rectangular form of a complex number is \(A + jB\), where \(A\) and \(B\) are positive, what is the polar form of the complex number?
### Options for Polar Form
1. \[
\sqrt{(A + B)^2} \angle \tan^{-1} \left(\frac{B}{A}\right)
\]
2. \[
\sqrt{A^2 + B^2} \angle \tan^{-1} \left(\frac{A}{B}\right)
\]
3. \[
(A^2 + B^2) \angle \tan^{-1} \left(\frac{B}{A}\right)
\]
4. \[
\sqrt{A^2 + B^2} \angle \tan^{-1} \left(\frac{B}{A}\right)
\]
### Explanation:
To convert from rectangular form to polar form, use the following:
- Magnitude: \( r = \sqrt{A^2 + B^2} \)
- Angle (in radians): \( \theta = \tan^{-1}\left(\frac{B}{A}\right) \)
In polar form, the complex number is expressed as \( r \angle \theta \).
### Correct Choice:
The correct polar form is:
\[
\sqrt{A^2 + B^2} \angle \tan^{-1} \left(\frac{B}{A}\right)
\]
This formula represents the magnitude and angle of the complex number in polar coordinates.
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