Complex Numbers

Question

The argument of the complex number z = 1 + i is

RankGuru · Accepted Answer

1. **Argument Formula**: The principal argument $	heta$ for $z = x + iy$ is given by $	an 	heta = \frac{y}{x}$, while considering the quadrant.
2. **Identify Values**: $x = 1, y = 1$.
3. **Quadrant Check**: Both $x$ and $y$ are positive, so the point $(1, 1)$ lies in the **$1^{st}$ quadrant**.
4. **Calculation**:
   - $	heta = 	an^{-1}(\frac{1}{1}) = 	an^{-1}(1)$
   - $	heta = \pi/4$.
5. **Polar Form**: This allows $z$ to be written as $\sqrt{2}(\cos \pi/4 + i \sin \pi/4)$.

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