Question

Find the rectangular form of the complex number given below. Use whatever identities are necessary to find the exact values. z = 2 cis 7π/8

Answer 1

The complex number is :


`z=2 \ cis ( (7 \pi )/(8) )=2(\cos(7 \pi )/(8) +i \sin (7 \pi )/(8))`.

Writing this point in the real x-y axis plane, we have:


`(x, y)=(2\cos(7 \pi )/(8) , 2 \sin (7 \pi )/(8))`.


`(7 \pi )/(8)` radians = (7/8)*180°=157.5°. We can find that:

cos(157.5°)=-0.924, so 2cos(157.5°)=-1.85

sin(157.5°)=0.383, so 2sin(157.5°)=0.77.



Answer: (-1.85, 0.77)