a+bi Form Calculator
Find a and b in a + bi from polar form.
Formula
a = r cos θ; b = r sin θ; z = a + bi.
Real part a ≈ (12)×cos((30)×pi÷180) · Imaginary coefficient b ≈ (12)×sin((30)×pi÷180)
How to use
- Enter the nonnegative magnitude r.
- Enter an angle from −360° to 360° or its radian equivalent.
- Read a and b and write a + bi; use a minus sign when b is negative.
Examples
- r = 12 and θ = 30° gives z ≈ 10.392305 + 6i.
Frequently asked questions
What does b represent?
The real coefficient multiplying i, where i² = −1.
Are degrees and radians supported?
Yes. Choose the unit before entering the angle.
What if r is zero?
Both components are zero for any angle; zero has no unique argument.
Sources
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