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 $z = -7 + 8i = r(cos theta + i sin theta), r = |z|, theta = text{arg } z$

$-7 = r cos theta$

$8 = r sin theta$

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

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

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

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

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