Question

find the modulus and argument of
1+√3i​

Answer 1

Answer:

Modulus is 4

Argument is 60°

Step-by-step explanation:

Given complex number is 1+√3i

Modulus of complex number x + iy is

$\sqrt{ {x}^{2} + {y}^{2} }$

Modulus of given complex number is

$\sqrt{ {1}^{2} + { \sqrt{3} }^{2} }$

$\sqrt{1 + 3}$

$\sqrt{4}$

$2$

Now argument of a complex number is

$tan^{ - 1} \frac{y}{x}$

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

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

$\frac{\pi}{3}$

=> 60°

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