Understanding Complex Solutions of cos (θ) = a

When a student first finds a complex solution to an equation such as cos (θ) = a (where a is greater than 1) it looks like a mighty bizarre answer, unlike anything seen previously. However when we look at the four sets of equations cos (θ) = a, cos (θ) = -a, cos (θ) = ai and cos (θ) = -ai together, we can see a familiar pattern emerge in their solutions (as can be seen by the thumbnail to this video), which helps enormously in understanding the overall family of complex solutions of cos (θ) = a etc.
Note: Prior to watching this video we suggest it would be useful to watch the Gresty Academy video 'How to Find all Complex Solutions of cos (z) = 3' which can be found at • How to Find all Comple... .
Further Note: The sister video to this video, entitled 'Understanding Complex Solutions of sin (θ) = a' (which should be watched subsequently to this video as it follows on from this one) can be found at • Understanding Complex ...
For more practice with complex numbers see our playlist 'Complex Numbers' at • Complex Numbers

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For more videos on complex numbers check out the Gresty Academy playlist 'Complex Numbers' at ua-cam.com/play/PLlX3COjsHPVC9MnNSwdVOfFk6zALYYEAm.html