Calculate complex numbers with instant conversion between rectangular form (a + bi) and polar/Euler form (r·e^(iθ)). Computes modulus, argument (in degrees and radians), complex conjugate, and reciprocal.
Also evaluates arithmetic operations between two complex numbers (addition, subtraction, multiplication, division), integer and fractional powers via De Moivre's theorem, principal square roots, complex exponential, and natural logarithm.
Frequently asked questions
What is the relationship between rectangular and polar form?
Rectangular form is z = a + bi. Polar form is z = r(cos θ + i sin θ) = r·e^(iθ), where r = √(a² + b²) and θ = atan2(b, a).
How does it compute complex powers?
Using De Moivre's formula: zⁿ = [r·e^(iθ)]ⁿ = rⁿ·e^(i·n·θ) = rⁿ(cos(nθ) + i sin(nθ)).
What is Euler's identity?
Setting r = 1 and θ = π yields e^(iπ) + 1 = 0, connecting five fundamental mathematical constants.
中文说明
全功能复数运算与形式互转工具：支持代数形式 (a + bi) 与极坐标/欧拉形式 (r·e^(iθ)) 实时双向互转，计算复数模长、辐角（角度与弧度）、共轭复数与倒数。
同时支持两复数间的四则运算（加减乘除），基于棣莫弗定理（De Moivre's formula）计算高阶幂次，以及主平方根、复指数函数 e^z 与复数主对数 Ln(z)。
常见问题
复数的代数形式与极坐标形式是如何转换的？
代数形式为 z = a + bi；极坐标/欧拉形式为 z = r·e^(iθ) = r(cos θ + i sin θ)，其中模长 r = √(a² + b²)，辐角 θ = atan2(b, a)。
复数的高次幂是如何计算的？
利用棣莫弗定理（De Moivre's formula）：zⁿ = rⁿ[cos(nθ) + i sin(nθ)]，通过极坐标进行乘方运算既稳定又精确。
什么是欧拉恒等式？
当取模长 r = 1、辐角 θ = π 时，由 e^(iθ) = cos θ + i sin θ 可得著名公式 e^(iπ) + 1 = 0，将数学中最重要的五大常数融为一体。