Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.

Question

Quizplus · Accepted Answer

To perform the indicated operation using trigonometric form, we can convert the given complex numbers to trigonometric form, multiply the magnitudes and add the angles.

Let's first find the trigonometric form of the given complex numbers:
A) $r = \sqrt{5^2+(-12)^2} = 13$, $	heta = \arctan\left(\frac{-12}{5}ight) = -1.1760$
$\Rightarrow 11e^{j(-1.1760)}$
B) $r = \sqrt{5^2+(-4)^2} = \sqrt{41}$, $	heta = \arctan\left(\frac{-4}{5}ight) = -0.6747$
$\Rightarrow 11e^{j(-0.6747)}$
C) $r = \sqrt{5^2+3^2} = \sqrt{34}$, $	heta = \arctan\left(\frac{3}{5}ight) = 0.5404$
$\Rightarrow 11e^{j(0.5404)}$
D) $r = \sqrt{5^2+2^2} = \sqrt{29}$, $	heta = \arctan\left(\frac{2}{5}ight) = 0.3851$
$\Rightarrow 11e^{j(0.3851)}$
E) $r = \sqrt{5^2+1^2} = \sqrt{26}$, $	heta = \arctan\left(\frac{1}{5}ight) = 0.1974$
$\Rightarrow 11e^{j(0.1974)}$

Now, we can multiply the magnitudes and add the angles to get the trigonometric form of the product:
$11e^{-j\pi/4}\cdot 11e^{-j0.6747} = 121e^{-j(0.6747+\pi/4)}$
$= 121e^{-j0.9614}$
$\Rightarrow 11ec8271\_dff6\_a079\_9e7c\_bbb0a713972f\_TB34225555\_00$

Perform the Indicated Operation Using Trigonometric Form