Question

Given w = 1 + i, what is arg (w) and |w|? Explain how you got your answer.

Answer 1

Answer:

arg (w)=π/4 and  |w|=√2

Step-by-step explanation:

If z= x+iy is a complex number, then |z| is given by √ ( x²+y² ).

And the argument (z) is given by Ф = tan⁻¹ ( y/x ) where -π < x < π.

Now, in our case w= 1+i i.e. x=1 and y=1.

Therefore, arg (w) = tan⁻¹ (1/1) = π/4 and |w|=√ ( 1²+1² ) = √2 (Answer)