Complex Numbers and Their Operations

Both are always positive.

Both can be expressed as a combination of two distinct parts.

Both have no real-world applications.

Both are used in geometry.

The imaginary unit, which is the square root of -1.

The real part of the number.

The sum of the real and imaginary parts.

The coefficient of the real part.

Multiply them together.

Divide the real part by the imaginary part.

Subtract the imaginary part from the real part.

Add the real parts together and the imaginary parts together.

An imaginary number.

A real number.

Zero.

A new complex number with the real and imaginary parts subtracted separately.

Divide the real part by the imaginary part.

Use the distributive property to expand the product.

Subtract the imaginary parts.

Add the real parts.

0

1

-1

i

To eliminate the imaginary part.

To simplify the expression.

To make the calculation faster.

To avoid confusion and ensure accuracy.

The real parts cancel out, leaving an imaginary number.

The result is always zero.

The imaginary parts cancel out, leaving a real number.

The result is always a complex number.

It simplifies the expression to a single number.

It helps in further calculations and understanding the structure.

It reduces the number of terms.

It makes the expression easier to read.

Only addition and subtraction.

Generalizing multiplication using algebraic expressions.

Avoiding the use of imaginary numbers.

Only focusing on real numbers.