Question

find modulus and amplitude of 1+i (step by step)

Answer 1

this is ur answer of question

Answer 2

Answer:

Modulus - $|Z|=\sqrt 2$

Amplitude - $\theta=\frac{\pi}{4}$

Step-by-step explanation:

To find : The modulus and amplitude of 1+i ?

Solution :

If z=a+ib is any complex number such that a∈R, b∈R then the

Modulus of complex number, |Z| is given by $|Z|=\sqrt{a^2+b^2}$

Amplitude of the complex number, θ is given by, $\theta= \tan^{-1}(\frac{b}{a})$

On comparing, a=1 and b=1

$|Z|=\sqrt{a^2+b^2}=\sqrt{1^2+1^2}=\sqrt{2}$

$\theta=\tan^{-1}(\frac{b}{a})=\tan^{-1}(\frac{1}{1})=\tan^{-1}\tan(\frac{\pi}{4})$

$\theta=\frac{\pi}{4}$