Question

Please! Convert the complex number from rectangular form to polar form. Show all work for full credit.

z= -14 + 8i
Please explain!

Answer 1

z = 2 sqrt(65) (cos( -.52) +i sin (-.52) )

Explanation:

to find the radius = sqrt(a^2 +b^2)

r = sqrt((-14^2 +8^2))

r = sqrt( 196+ 64)

r = sqrt (260)

r = sqrt(4*65)

r = 2sqrt(65)

theta = arctan (b/a)

theta = arctan (8/-14)

theta = arctan (-4/7)

theta =-.52 radians

z = r (cos theta + i sin theta)

z = 2 sqrt(65) (cos( -.52) +i sin (-.52) )