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Square of a Complex Number
## Formula
If:
$$z=a+ib$$
then:
$$z^2=(a^2-b^2)+2abi$$
Therefore:
$$\operatorname{Re}(z^2)=a^2-b^2$$
$$\operatorname{Im}(z^2)=2ab$$
## Usage
- Used to expand powers of complex numbers and compare real and imaginary parts.
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Square of a Complex Number
## Formula
If:
$$z=a+ib$$
then:
$$z^2=(a^2-b^2)+2abi$$
Therefore:
$$\operatorname{Re}(z^2)=a^2-b^2$$
$$\operatorname{Im}(z^2)=2ab$$
## Usage
- Used to expand powers of complex numbers and compare real and imaginary parts.
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