Let z = −2√3 + 6ia) Express z|z| in polar form.b) Determine z48 in polar form, in terms of its principal argument.

Question

Let z = −2√3 + 6ia) Express z|z| in polar form.b) Determine z48 in polar form, in terms of its principal argument.
🧐 Not the exact question you are looking for?Go ask a question

Solution 1

a) To express z in polar form, we first need to find the magnitude (r) and the argument (θ) of z.

The magnitude of z is given by |z| = √((Re(z))^2 + (Im(z))^2) = √((-2√3)^2 + (6)^2) = √(12 + 36) = √48 = 4√3.

The argument of z is given by θ = atan(Im(z)/Re(z)) = atan(-6/-2√3) = atan(√3/2) = π/3.

S Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

This problem has been solved

Similar Questions

Let z = −2√3 + 6ia) Express z|z| in polar form.b) Determine z48 in polar form, in terms of its principal argument.

Let α = −1 + j and β = 4 − j. In each case, solve for z.(a) z − β∗ = Im( α22β + j)(b) z4 = α

Write the exponential form and the principal argument of the following complex numbers.(i) z =i/(−2 − 2i)

Write the exponential form and the principal argument of the following complex numbers.(ii) z = (√3 − i)^6

7 marks) Let α = −1 + j and β = 4 − j. In each case, solve for z.(a) z − β∗ = Im( α22β + j)(b) z4 = α

1/3