Question

Write the complex number, z=-5+5i in polar form with the angle expressed in radians from 0 to 2(pi).

Answer 1

\[-5 = rcos \theta\]
\[5 = rsin \theta\]
solve for angle by substitution
\[5 = -5\frac{\sin \theta}{\cos \theta}\]
\[\tan \theta = -1\]
\[\theta = \frac{3\pi}{4}\]
\[r = \frac{5}{\sin(3\pi/4)} = \frac{5}{\sqrt{2}/2} = 5\sqrt{2}\]

Answer 2

there is an easier way as well using triangle

then use pythagorean thm to find r
tangent to find angle

Answer 3

sqrt of 50

Answer 4

which simplifies to 5sqrt2