__maths__>__Complex Numbers__>__Properties of Complex Number Arithmetic__### Algebraic Identities for Complex numbers

The algebraic identities of complex number is same as that for real numbers.

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Which of the following are examples of algebraic identities?

- `(a+b)^2 = a^2+2ab+b^2`
- `(a-b)^2 = a^2-2ab+b^2`
- `a^2-b^2 = (a+b)(a-b)`
- all the above
- all the above

The answer is 'all the above'

If an algebraic identity is true for real numbers, will that be true for complex numbers?

- No, it will not be true at all
- Yes, for all identities with four fundamental operations
- Yes, for all identities with four fundamental operations

The answer is 'Yes, for all identities with four fundamental operations'.

The four fundamental operations like

• addition,

• subtraction,

• multiplication, and

• division define the properties

• associative,

• commutative

• distributive.

The algebraic identities employ the properties of the operations given above. Between real numbers and complex numbers the properties are same. So the algebraic identities will hold true.

• Algebraic identities are same as that of real numbers.

**Algebraic Identities: ** `(z_1+z_2)^2 = z_1^2+ 2z_1z_2+z_2^2`

`(z_1-z_2)^2 = z_1^2 - 2z_1z_2+z_2^2`

`(z_1+z_2)(z_1-z_2) = z_1^2 - z_2^2`

`(z_1+z_2)^3 = z_1^3+z_2^3+ 3z_1^2z_2+ 3z_1z_2^2`

and so on.

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