Question

(v) Find the modulus and amplitude of the
complex numbers 1+i√3 ​

Answer 1

★ Answer ★

★ Modulus ★

Modulus of a complex number in the form of z=x + iy where x,y∈R is given as :

|z| = $\sqrt{x^{2}+y^{2} }$

Substituting x = 1 and y = $\sqrt{3}$

Modulus of the complex number = $\sqrt{1^{2} +3}$ = 2

★ Amplitude ★

Amplitude of a complex number in the form of z= x + iy is:

Amplitude = $tan^{-1}(\frac{y}{x} )$

= $tan^{-1}\sqrt{3}$

= $\frac{\pi }{3}$

Answer 2

Step-by-step explanation:

Modulus of a complex number in the form of z=x + iy where x,y∈R is given as :

|z| = \sqrt{x^{2}+y^{2} }

x

2

+y

2

Substituting x = 1 and y = \sqrt{3}

3

Modulus of the complex number = \sqrt{1^{2} +3}

1

2

+3

= 2

Amplitude of a complex number in the form of z= x + iy is:

Amplitude = tan^{-1}(\frac{y}{x} )tan

−1

(

x

y

)

= tan^{-1}\sqrt{3}tan

−1

3

= \frac{\pi }{3}

3

π