How do you convert #(2, 3pi/4)# into cartesian form?

1 Answer
Anthony X
Dec 11, 2016

#-sqrt2 + sqrt2 i#

Explanation:

Currently the coordinate #(2,3pi/4)# is in polar form, which is #(r,theta)# form.

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We could use a funky looking graph like this in order to plot that point.

However, if we want to convert the coordinate into a more familiar rectangular or cartesian form, we need to get the coordinate into #a+bi# form.

we can use the formula

#r(costheta + isintheta)#

to get the number into

#rcostheta + rsinthetai#

This is because #rcostheta# is the horizontal component of the magnitude of #r#, and #rsintheta# is the vertical component of #r#.

Plugging in for r and theta, in radians, we get

#-sqrt2 + sqrt2 i#

If we were to graph the point, we would do something like this, but instead of 2, we would plot the x axis at #-sqrt2#, and similarly the y coordinate at #sqrt2#

enter image source here

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