Question

Given that Z=√3 + √3 i, write Z in Euler form​

Answer 1

To write Z in Euler form, we first need to find its magnitude and argument.

The magnitude of Z is given by:

|Z| = √(Re(Z)^2 + Im(Z)^2)

where Re(Z) is the real part of Z, and Im(Z) is the imaginary part of Z.

In this case:

Re(Z) = √3

Im(Z) = √3 i

So:

|Z| = √(√3^2 + (√3)^2) = √(3 + 3) = √6

The argument of Z is given by:

arg(Z) = tan^(-1)(Im(Z) / Re(Z))

In this case:

arg(Z) = tan^(-1)((√3) / √3) = tan^(-1)(1) = π/4

Therefore, Z in Euler form is:

Z = |Z| e^(i arg(Z)) = √6 e^(i π/To write Z in Euler form, we first need to find its magnitude and argument.

The magnitude of Z is given by:

|Z| = √(Re(Z)^2 + Im(Z)^2)

where Re(Z) is the real part of Z, and Im(Z) is the imaginary part of Z.

In this case:

Re(Z) = √3

Im(Z) = √3 i

So:

|Z| = √(√3^2 + (√3)^2) = √(3 + 3) = √6

The argument of Z is given by:

arg(Z) = tan^(-1)(Im(Z) / Re(Z))

In this case:

arg(Z) = tan^(-1)((√3) / √3) = tan^(-1)(1) = π/4

Therefore, Z in Euler form is:

Z = |Z| e^(i arg(Z)) = √6 e^(i π/4)