Find the argument of 2+3i

Question

ScanSolve AI Tutor · Accepted Answer

To find the argument of a complex number $z = x + yi$ , we use the formula $\arg(z) = \arctan\left(\frac{y}{x}\right)$ , considering the quadrant of the complex number.

Identify the real and imaginary parts of the complex number.
The given complex number is $z = 2 + 3i$ .
Here, the real part is $x = 2$ and the imaginary part is $y = 3$ .
Determine the quadrant of the complex number.
Since $x > 0$ and $y > 0$ , the complex number $2+3i$ lies in the first quadrant. Therefore, the principal argument will be directly given by $\arctan\left(\frac{y}{x}\right)$ .
Calculate the argument.
$\arg(z) = \arctan\left(\frac{3}{2}\right)$
Using a calculator,
$\arg(z) \approx 56.31^{\circ}$
In radians,
$\arg(z) \approx 0.9828 \text{ radians}$
The argument of $2+3i$ is approximately:
$56.31^{\circ} \text{ or } 0.9828 \text{ radians}$

Find the argument of 2+3i

Answer

Step-by-step solution

Identify the real and imaginary parts of the complex number.

Determine the quadrant of the complex number.

Calculate the argument.

Try one yourself

Still stuck on this one?

More Mathematics Questions