Question

What is the rectangular form of z= 40(cos(7pi/6)+ i sin(7pi/6))

Answer 1

Answer:

C. $z = -20\sqrt{3}-i\,20$

Step-by-step explanation:

The rectangular form of a complex number is represented by the following formula:

$z = a+i\,b$ (1)

Where each coefficient can be determined as function of the polar components:

$a = r\cdot \cos \theta$ (2)

$b = r\cdot \sin \theta$ (3)

Where:

$r$ - Magnitude of the complex number, dimensionless.

$\theta$ - Direction of the complex number, measured in radians.

If we know that $r = 40$ and $\theta = \frac{7\pi}{6}$, then the rectangular form of the number is:

$a = 40\cdot \cos \frac{7\pi}{6}$

$a = -20\sqrt{3}$

$b = 40\cdot \sin \frac{7\pi}{6}$

$b = -20$

The rectangular form of $z=40\cdot\left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6}\right)$ is $z = -20\sqrt{3}-i\,20$. The correct answer is C.