Complex number in trigonometric form

Question

write the complex number z=2+4i in trigonemetric form. Express the angle  θ in radians where 0 is equal to or lesser than θ2pi.

z= __(cos__+isin__)

please help me fill in the blanks

 

Answer 1

z = 2 + 4i

Plot the point (2,4)

z = r(cosθ + isinθ)

r = distance from (0,0) to (2,4) = √[2² + 4²] = 2√5

θ = angle with vertex at (0,0) having the positive x-axis as its initial side and terminal side passing through (2,4)

θ = Tan^-1(4/2) = 1.107

So, 2 + 4i = 2√5[cos1.107 + isin1.107]