The angle between the complex numbers 2+2i and -7

Consider the right triangle formed by the complex number in the Argand-Gauss plane and it's projections on the axis. – José Siqueira Nov 12 '13 at 17:21

In particular what is the definition of sine of theta in terms of the known sides of the above mentioned right triangle? – Adam Nov 12 '13 at 17:27

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3 Answers

1

Consider the following Argand-diagram

enter image description here

The y-axis is the imaginary axis and the x-axis is the real one. The complex number in question is

x+yi

To figure out θ, consider the right-triangle formed by the two-coordinates on the plane (illustrated in red). Let θ be the angle formed with the real axis.

tanθ=yx

⟹tan−1(yx)

The hypotenuse of the triangle will be

x2+y2−−−−−−√

Therefore,

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