Question

If z = 1 + 2i , then the argument of z is

Answer 1

Answer on Question #58288 – Math – Complex Analysis

Question

If $z = 1 + 2i$, then the argument of $z$ is?

Solution

z = 1 + 2i,

Re z=1>0; Im z =2>0,

$$\tan(\arg z) = \frac{\operatorname{Im} z}{\operatorname{Re} z} = \frac{2}{1} = 2, \text{ so } \arg z = \arctan(2);$$ $$\arctan(2) \approx 63.43{}^\circ.$$

Answer: arg z = $\arctan(2) \approx 63.43{}^\circ$.

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