Question

Find 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} }

x

2

+y

2

Modulus of given complex number is

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

1

2

+

3

2

\sqrt{1 + 3}

1+3

\sqrt{4}

4

22

Now argument of a complex number is

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

−1

x

y

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

−1

1

3

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

−1

3

\frac{\pi}{3}

3

π

=> 60°