# What is the trigonometric form of  (2-i)*(3+i) ?

Oct 8, 2016

5sqrt2cis(-8°8')

#### Explanation:

Let $z = \left(2 - i\right) \cdot \left(3 + i\right) = 6 + 2 i - 3 i - {i}^{2} = 7 + \left(- 1\right) i$

Modulus:
$| z | = \sqrt{{7}^{2} + {\left(- 1\right)}^{2}} = \sqrt{50} = 5 \sqrt{2}$

Argument:
Let $a r g \left(z\right) = \Theta$
$\tan \Theta = - \frac{1}{7}$
Theta=-8°8'

• Be careful when finding the argument, it is always good to plot the complex number on an Argand diagram to determine which quadrant it is in, just so that you write the correct principal argument.

:.z=5sqrt2(cos(-8°8')+isin(-8°8'))=5sqrt2cis(-8°8')