Convertools

Imaginary Part from Magnitude and Phase (Degrees)

Calculate the imaginary component of a complex number from magnitude and phase angle in degrees.

Author

Prof. Kenji Tanaka

Math editorial contributor

Japanese materials scientist at Kyoto University, known for breakthroughs in sustainable polymer research

Reviewed by

Dr. Emeka Nwosu

Math content reviewer

Nigerian legal scholar with an SJD from Yale, focused on international trade law and African continental free trade agreements

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

Table of Contents

  1. Reference values
  2. Calculator
  3. Reference table
  4. FAQs
  5. Methodology and review
  6. Related conversions

5 Magnitude Magnitude; 0 deg Phase Angle (Degrees) =

0 Imaginary Part

Representative value from the Imaginary Part from Magnitude and Phase (Degrees) reference table.

Reference Values

Browse 105 reference values with individual detail pages for quick lookup.

Browse all reference values

Imaginary Part from Magnitude and Phase (Degrees)

Calculate the imaginary component of a complex number from magnitude and phase angle in degrees.

Calculated Result

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Reference Table

Use this complete table for quick lookup and internal linking to specific value pages.

Imaginary Part from Magnitude and Phase (Degrees) Reference
ScenarioImaginary Part
0 Magnitude Magnitude; -180 deg Phase Angle (Degrees)-0 Imaginary Part
0 Magnitude Magnitude; -150 deg Phase Angle (Degrees)-0 Imaginary Part
0 Magnitude Magnitude; -120 deg Phase Angle (Degrees)-0 Imaginary Part
0 Magnitude Magnitude; -90 deg Phase Angle (Degrees)-0 Imaginary Part
0 Magnitude Magnitude; -60 deg Phase Angle (Degrees)-0 Imaginary Part
0 Magnitude Magnitude; -45 deg Phase Angle (Degrees)-0 Imaginary Part
0 Magnitude Magnitude; -30 deg Phase Angle (Degrees)-0 Imaginary Part
0 Magnitude Magnitude; 0 deg Phase Angle (Degrees)0 Imaginary Part
0 Magnitude Magnitude; 30 deg Phase Angle (Degrees)0 Imaginary Part
0 Magnitude Magnitude; 45 deg Phase Angle (Degrees)0 Imaginary Part
0 Magnitude Magnitude; 60 deg Phase Angle (Degrees)0 Imaginary Part
0 Magnitude Magnitude; 90 deg Phase Angle (Degrees)0 Imaginary Part
0 Magnitude Magnitude; 120 deg Phase Angle (Degrees)0 Imaginary Part
0 Magnitude Magnitude; 150 deg Phase Angle (Degrees)0 Imaginary Part
0 Magnitude Magnitude; 180 deg Phase Angle (Degrees)0 Imaginary Part
1 Magnitude Magnitude; -180 deg Phase Angle (Degrees)-0 Imaginary Part
1 Magnitude Magnitude; -150 deg Phase Angle (Degrees)-0.5 Imaginary Part
1 Magnitude Magnitude; -120 deg Phase Angle (Degrees)-0.866025 Imaginary Part
1 Magnitude Magnitude; -90 deg Phase Angle (Degrees)-1 Imaginary Part
1 Magnitude Magnitude; -60 deg Phase Angle (Degrees)-0.866025 Imaginary Part
1 Magnitude Magnitude; -45 deg Phase Angle (Degrees)-0.707107 Imaginary Part
1 Magnitude Magnitude; -30 deg Phase Angle (Degrees)-0.5 Imaginary Part
1 Magnitude Magnitude; 0 deg Phase Angle (Degrees)0 Imaginary Part
1 Magnitude Magnitude; 30 deg Phase Angle (Degrees)0.5 Imaginary Part
1 Magnitude Magnitude; 45 deg Phase Angle (Degrees)0.707107 Imaginary Part
1 Magnitude Magnitude; 60 deg Phase Angle (Degrees)0.866025 Imaginary Part
1 Magnitude Magnitude; 90 deg Phase Angle (Degrees)1 Imaginary Part
1 Magnitude Magnitude; 120 deg Phase Angle (Degrees)0.866025 Imaginary Part
1 Magnitude Magnitude; 150 deg Phase Angle (Degrees)0.5 Imaginary Part
1 Magnitude Magnitude; 180 deg Phase Angle (Degrees)0 Imaginary Part
2 Magnitude Magnitude; -180 deg Phase Angle (Degrees)-0 Imaginary Part
2 Magnitude Magnitude; -150 deg Phase Angle (Degrees)-1 Imaginary Part
2 Magnitude Magnitude; -120 deg Phase Angle (Degrees)-1.732051 Imaginary Part
2 Magnitude Magnitude; -90 deg Phase Angle (Degrees)-2 Imaginary Part
2 Magnitude Magnitude; -60 deg Phase Angle (Degrees)-1.732051 Imaginary Part
2 Magnitude Magnitude; -45 deg Phase Angle (Degrees)-1.414214 Imaginary Part
2 Magnitude Magnitude; -30 deg Phase Angle (Degrees)-1 Imaginary Part
2 Magnitude Magnitude; 0 deg Phase Angle (Degrees)0 Imaginary Part
2 Magnitude Magnitude; 30 deg Phase Angle (Degrees)1 Imaginary Part
2 Magnitude Magnitude; 45 deg Phase Angle (Degrees)1.414214 Imaginary Part
2 Magnitude Magnitude; 60 deg Phase Angle (Degrees)1.732051 Imaginary Part
2 Magnitude Magnitude; 90 deg Phase Angle (Degrees)2 Imaginary Part
2 Magnitude Magnitude; 120 deg Phase Angle (Degrees)1.732051 Imaginary Part
2 Magnitude Magnitude; 150 deg Phase Angle (Degrees)1 Imaginary Part
2 Magnitude Magnitude; 180 deg Phase Angle (Degrees)0 Imaginary Part
5 Magnitude Magnitude; -180 deg Phase Angle (Degrees)-0 Imaginary Part
5 Magnitude Magnitude; -150 deg Phase Angle (Degrees)-2.5 Imaginary Part
5 Magnitude Magnitude; -120 deg Phase Angle (Degrees)-4.330127 Imaginary Part
5 Magnitude Magnitude; -90 deg Phase Angle (Degrees)-5 Imaginary Part
5 Magnitude Magnitude; -60 deg Phase Angle (Degrees)-4.330127 Imaginary Part
5 Magnitude Magnitude; -45 deg Phase Angle (Degrees)-3.535534 Imaginary Part
5 Magnitude Magnitude; -30 deg Phase Angle (Degrees)-2.5 Imaginary Part
5 Magnitude Magnitude; 0 deg Phase Angle (Degrees)0 Imaginary Part
5 Magnitude Magnitude; 30 deg Phase Angle (Degrees)2.5 Imaginary Part
5 Magnitude Magnitude; 45 deg Phase Angle (Degrees)3.535534 Imaginary Part
5 Magnitude Magnitude; 60 deg Phase Angle (Degrees)4.330127 Imaginary Part
5 Magnitude Magnitude; 90 deg Phase Angle (Degrees)5 Imaginary Part
5 Magnitude Magnitude; 120 deg Phase Angle (Degrees)4.330127 Imaginary Part
5 Magnitude Magnitude; 150 deg Phase Angle (Degrees)2.5 Imaginary Part
5 Magnitude Magnitude; 180 deg Phase Angle (Degrees)0 Imaginary Part
10 Magnitude Magnitude; -180 deg Phase Angle (Degrees)-0 Imaginary Part
10 Magnitude Magnitude; -150 deg Phase Angle (Degrees)-5 Imaginary Part
10 Magnitude Magnitude; -120 deg Phase Angle (Degrees)-8.660254 Imaginary Part
10 Magnitude Magnitude; -90 deg Phase Angle (Degrees)-10 Imaginary Part
10 Magnitude Magnitude; -60 deg Phase Angle (Degrees)-8.660254 Imaginary Part
10 Magnitude Magnitude; -45 deg Phase Angle (Degrees)-7.071068 Imaginary Part
10 Magnitude Magnitude; -30 deg Phase Angle (Degrees)-5 Imaginary Part
10 Magnitude Magnitude; 0 deg Phase Angle (Degrees)0 Imaginary Part
10 Magnitude Magnitude; 30 deg Phase Angle (Degrees)5 Imaginary Part
10 Magnitude Magnitude; 45 deg Phase Angle (Degrees)7.071068 Imaginary Part
10 Magnitude Magnitude; 60 deg Phase Angle (Degrees)8.660254 Imaginary Part
10 Magnitude Magnitude; 90 deg Phase Angle (Degrees)10 Imaginary Part
10 Magnitude Magnitude; 120 deg Phase Angle (Degrees)8.660254 Imaginary Part
10 Magnitude Magnitude; 150 deg Phase Angle (Degrees)5 Imaginary Part
10 Magnitude Magnitude; 180 deg Phase Angle (Degrees)0 Imaginary Part
20 Magnitude Magnitude; -180 deg Phase Angle (Degrees)-0 Imaginary Part
20 Magnitude Magnitude; -150 deg Phase Angle (Degrees)-10 Imaginary Part
20 Magnitude Magnitude; -120 deg Phase Angle (Degrees)-17.320508 Imaginary Part
20 Magnitude Magnitude; -90 deg Phase Angle (Degrees)-20 Imaginary Part
20 Magnitude Magnitude; -60 deg Phase Angle (Degrees)-17.320508 Imaginary Part
20 Magnitude Magnitude; -45 deg Phase Angle (Degrees)-14.142136 Imaginary Part
20 Magnitude Magnitude; -30 deg Phase Angle (Degrees)-10 Imaginary Part
20 Magnitude Magnitude; 0 deg Phase Angle (Degrees)0 Imaginary Part
20 Magnitude Magnitude; 30 deg Phase Angle (Degrees)10 Imaginary Part
20 Magnitude Magnitude; 45 deg Phase Angle (Degrees)14.142136 Imaginary Part
20 Magnitude Magnitude; 60 deg Phase Angle (Degrees)17.320508 Imaginary Part
20 Magnitude Magnitude; 90 deg Phase Angle (Degrees)20 Imaginary Part
20 Magnitude Magnitude; 120 deg Phase Angle (Degrees)17.320508 Imaginary Part
20 Magnitude Magnitude; 150 deg Phase Angle (Degrees)10 Imaginary Part
20 Magnitude Magnitude; 180 deg Phase Angle (Degrees)0 Imaginary Part
50 Magnitude Magnitude; -180 deg Phase Angle (Degrees)-0 Imaginary Part
50 Magnitude Magnitude; -150 deg Phase Angle (Degrees)-25 Imaginary Part
50 Magnitude Magnitude; -120 deg Phase Angle (Degrees)-43.30127 Imaginary Part
50 Magnitude Magnitude; -90 deg Phase Angle (Degrees)-50 Imaginary Part
50 Magnitude Magnitude; -60 deg Phase Angle (Degrees)-43.30127 Imaginary Part
50 Magnitude Magnitude; -45 deg Phase Angle (Degrees)-35.355339 Imaginary Part
50 Magnitude Magnitude; -30 deg Phase Angle (Degrees)-25 Imaginary Part
50 Magnitude Magnitude; 0 deg Phase Angle (Degrees)0 Imaginary Part
50 Magnitude Magnitude; 30 deg Phase Angle (Degrees)25 Imaginary Part
50 Magnitude Magnitude; 45 deg Phase Angle (Degrees)35.355339 Imaginary Part
50 Magnitude Magnitude; 60 deg Phase Angle (Degrees)43.30127 Imaginary Part
50 Magnitude Magnitude; 90 deg Phase Angle (Degrees)50 Imaginary Part
50 Magnitude Magnitude; 120 deg Phase Angle (Degrees)43.30127 Imaginary Part
50 Magnitude Magnitude; 150 deg Phase Angle (Degrees)25 Imaginary Part
50 Magnitude Magnitude; 180 deg Phase Angle (Degrees)0 Imaginary Part

Frequently Asked Questions

Common questions about Imaginary Part from Magnitude and Phase (Degrees), formulas, and typical use cases.

What does the Imaginary Part from Magnitude and Phase (Degrees) calculator do?

It helps with converting polar complex form into rectangular imaginary component.

What formula does the Imaginary Part from Magnitude and Phase (Degrees) calculator use?

Imaginary part = magnitude × sin(phase angle in degrees).

What inputs are valid?

Magnitude must be non-negative; phase angle can be any finite degree value.

When would I use this?

converting polar complex form into rectangular imaginary component

Methodology and Review

This page combines a live calculator, precomputed reference values, and FAQ content from the same conversion definition to reduce mismatch between calculator output and lookup tables.

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