Shortcut Methods
JEE Main
Shortcut Methods and Tricks:

To find the modulus of a complex number, simply use the formula $\sqrt{a^2 + b^2}$, where (a) and (b) are the real and imaginary parts of the complex number, respectively.

To find the argument of a complex number, use the formula $\tan^{1}(\frac{b}{a})$, where (a) and (b) are the real and imaginary parts of the complex number, respectively.

To find the complex conjugate of a complex number, simply change the sign of the imaginary part.
CBSE Board Exams
Shortcut Methods and Tricks:
 To find the modulus of a complex number, simply use the formula $\sqrt{a^2 + b^2}$, where (a) and (b) are the real and imaginary parts of the complex number, respectively.
 To find the argument of a complex number, use the formula $\tan^{1}(\frac{b}{a})$, where (a) and (b) are the real and imaginary parts of the complex number, respectively.
 To find the complex conjugate of a complex number, simply change the sign of the imaginary part.