1Write the complex number in polar form with argument betwee

1.Write the complex number in polar form with argument between 0 and 2.

i

7-7i

Solution

3 +3sqrt3i

recatngular form z = x+iy

Polar form : z== re^i*x

r =sqrt(x^2 +y^2) = sqrt(3^3 +27) =6

x = tan^-1(3sqrt3/3) = tan^-1(sqrt3) = pi/3

So,Polar form : z = 6e^(pi/3)i

z = sqrt7 - sqrt7*i

r = sqrt( sqrt7^2 +sqrt7^2) = sqrt14

x = tan^-1(-sqrt7/sqrt7) = tan^-1(-1) = 3pi/4

Polar form : z = sqrt(14)e^3pi/4)i