Complex Numbers

Easymathematics

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

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π/4

π/2

π/6

π/3

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About This Question

Subject: mathematics
Chapter: complex numbers and quadratic equations
Topic: complex numbers
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

π/4

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

This easy difficulty mathematics question is from the chapter complex numbers and quadratic equations, covering the topic of complex numbers. It appeared in the 2025 exam.

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