What is the trigonometric form of # (-7+8i) #?

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Answer 1 · 2015-12-21T17:45:10

#z = sqrt 113 (cos theta + i sin theta), theta = pi - arctan frac{8}{7}#

We search for #z = -7 + 8i = r(cos theta + i sin theta), r = |z|, theta = text{arg } z#

#-7 = r cos theta#

#8 = r sin theta#

#7^2 + 8^2 = 113 = r^2#

#8/-7 = tan theta ; pi/2 < theta < pi#

#tan (pi - theta) = sin (pi - theta) / cos (pi - theta) = sin theta /- cos theta = - tan theta = 8/7#

#theta = pi - arctan frac{8}{7}#