write the complesx number in trigonometric form? (40)?

Question

5+5i

Answer 1

r = sqrt(a^2 + b^2)
tan(theta) = b/a

r = sqrt(25+25) = sqrt50 = 5sqrt2
tan(theta) = 5/5 = 1
we know that theta = 45degrees or pi/4 radians

trig form

z = 5sqrt (cos pi/4 + i sin pi/4)

Answer 2

Draw a right angled triangle of sides 5 , 5 and Z
Z is hypotenuse and is required complex number.
Z = 5 + 5i
|Z| = √50
Angles in triangle are 45°,45° and 90°
Z = √50 angle 45°
Z = √50.(cos 45° + i sin 45°)
Check
Z = √50.(1/√2 + i 1/√2 )
Z = (√50/√2).(1 + i)
Z = 5.(1 + i) as required