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Complex Numbers Definition Calculator

Online complex number tool: enter real part a and imaginary part b to write and classify the number.

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z=a+bi, i²=−1
Complex z
a
b

📖 Tutorial | Complex Numbers

1. Definition
A number z=a+bi is complex, with real part a, imaginary part b and i²=−1; it corresponds to the point (a,b).
2. Formula & Notation
a,bReal, imaginary
3. Properties & Laws
  • b=0 real;
  • b≠0 imaginary;
  • a=0,b≠0 pure imaginary;
  • Point in the complex plane.
4. Steps
  1. Enter a,b;
  2. Click "OK";
  3. Or click "Load Example".
5. Worked Examples
Example: a=3,b=4: z=3+4i (imaginary).
6. Common Pitfalls
Pure needs real part 0;
Imaginary part is b, not bi;
i²=−1.

❓ FAQ | Complex Numbers

Form?
a+bi.
i?
i²=−1.
Types?
Real/imaginary/pure.
Geometry?
Point.
Example?
3+4i.
Zero?
Both 0.