Complex Numbers and Their Operations

It helps in visualizing patterns.

It makes numbers smaller.

It simplifies calculations.

It eliminates imaginary parts.

As the z-coordinate

As the x-coordinate

As the origin

As the y-coordinate

It negates the real part of the number.

It doubles the magnitude of the number.

It reflects the number across the real axis.

It rotates the number by 90 degrees.

Both parts

The real part

The imaginary part

Neither part

4 + 3i

3 + 3i

2 + 3i

4 + 2i

Neither are commutative.

Addition is commutative, subtraction is not.

Both are commutative.

Subtraction is commutative, addition is not.

It remains in the same position.

It moves to the right and down.

It moves to the left and down.

It moves to the left and up.

2 - i

2 + i

1 + 2i

4 + 3i

Mirroring a number across the real axis

Doubling the magnitude of a number

Rotating a number around the origin

Negating both real and imaginary parts

A rotation around the origin

A scaling of the magnitude

A movement in the opposite direction of w

A reflection across the imaginary axis