Quickly convert complex numbers from their standard rectangular form (a + bi) to their trigonometric (polar) form (r(cos θ + i sin θ)). Our calculator finds the magnitude (r) and argument (θ), simplifying complex number conversions for mathematics students and professionals alike, providing results in both degrees and radians.
Formula:
A complex number in standard rectangular form is expressed as z = a + bi, where 'a' is the real part and 'b' is the imaginary part. Its equivalent trigonometric (polar) form is z = r(cos θ + i sin θ), where:
- r (magnitude or modulus) = √(a2 + b2)
- θ (argument or angle) = atan2(b, a)
The atan2(y, x) function correctly determines the angle θ across all four quadrants, ensuring the correct argument for any complex number.