Find the polar form of the complex number 7 – 5i.

The polar form of x+yi =  r(cost+isint), where r =
sqrt(x^2+y^2).

cost = x/sqrt(x^2+y^2) , sint = 
y/(x^2+y^2).

r is called the modulus of x+yi and t is called the
aruement or ampitude of x+yi.

Therefore the given complex number,
x+yi = 7 - 5i

r = sqrt {(7^2+(-5)^2} = sqrt(25+49) =
sqrt74.

Therefore  cos t = 7/sqrt74 and sin t
=-5/sqrt74.

Therefore  t =  arc tan (-5/7) = -0.6204 rad
appr.

Therefore  7-5i = sqrt74{ cost+isint) , where t = -0.6204
rad.

7-5i = sqrt74({cos (arc tan (-5/7) +i sin arctan(-5/7)} in
polar form.