# What is the polar form of (42,77)?

Oct 6, 2016

$\sqrt{7693} c i s \left(1.071\right)$

#### Explanation:

Quick way of doing this: Use the Pol button on ur calculator and enter the coordinates.

If $z$ is the complex number,
Finding modulus:
$| z | = \sqrt{{42}^{2} + {77}^{2}} = \sqrt{7693}$

Finding argument:
Plot the point on an Argand diagram. This is important to ensure that you write the principal argument. We can see that the complex number is in the first quadrant, so no adjustments need to be made, but be wary when the point is in the 3rd/4th quadrants.

Arg$\left(z\right) = {\tan}^{-} 1 \left(\frac{77}{42}\right) = 1.071$ radians or 61°23'

Placing this in polar form,
$z = | z | c i s a r g \left(z\right) = \sqrt{7693} c i s 1.071$