Complex Numbers

Easymathematics

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

Select the correct option:

π/4

π/2

π/6

π/3

🔒 Solution Hidden from View

Submit your answer to unlock the detailed step-by-step solution.

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.

Looking for more practice? Explore all mathematics questions or browse complex numbers and quadratic equations questions on RankGuru.

Complex Numbers

Select the correct option:

Solution

🔒 Solution Hidden from View

More complex numbers Practice Questions

The principal argument of the complex number given by z = -1 + i times the square root of 3, express...

If z is a complex number satisfying the modulus relation |z - 3| = |z + 3|, then the point represent...

If z = 3 + 4i, then |z| equals

If |z - 2| = 2|z - 1|, then the locus of z is

If z is a complex number such that |z| = 1, then the value of (1 + z)/(1 + z̄) (where z̄ is the conj...

About This Question

Solution