What it covers
The complex number hub groups tools for arithmetic, conjugates, arguments, square roots, powers, and form conversion.
सूत्र
- Algebraic form: z = a + bi.
- Polar form: z = r(cos theta + i sin theta).
- Exponential form: z = re^(i theta).
इनपुट
- Real and imaginary parts.
- Magnitude and argument.
- Operation or conversion type.
उदाहरण
| Question | Suggested tool | Use |
|---|---|---|
| Modulus and angle of 3+4i | complex-argument / form converter | Position in the complex plane |
| (2+i)(1-3i) | complex-arithmetic | Complex multiplication |
| sqrt(-1) | complex-square-root | Complex roots |
परिणाम कैसे समझें
A complex result can be read as an algebraic expression or as a point/vector in the complex plane. Polar form is especially useful for multiplication, division, powers, and roots.
सामान्य गलतियाँ
- i^2 = -1.
- Arguments can have many equivalent angles.
- Complex roots often have multiple values.