00:01
In this problem, we have the complex number, r, e -power i -theta is equal to r times cosine of theta plus i -sign of theta, which is the demoever theorem.
00:11
So here the first complex number is z -1, which is equal to cosine pi over four plus i -sign pi -over -four, and this is equal to e -power i pi over four, because theta here is pi -over -four, and r is equal to one.
00:25
The second complex number is z2, which is equal to cosine 3 pi over 4, plus i sign 3 pi over 4, and this is equal to e -power 3 -i over 4, because here theta is 3 -5 over 4, and r is equal to 1.
00:43
So here the product, z1, times z2, is equal to e -power i pi over 4 times e -power 3 -i over 4, which is equal to e -power i pi over 4 plus 3 pi i over 4 and this is equal to e to the power pi i and now here the quotient z 1 over z2 is equal to e power pii over 4 over e power 3 pii over 4 and this is equal to e power pi i over 4 minus 3 pi i over 4 and this is equal to e power minus pii over 4 of 4 2.
01:23
This is for the first part of the problem.
01:27
Now the second part of the problem is z which is equal to 4 times cosine 160 degrees plus i sign 160 degrees and the second complex number is z 2 which is equal to 2 times cosine 70 degrees plus i sign 70 degrees...