Put in polar form z -3(cos(6) + i sin(6)). What is its principle argument, Arg(z)?

The complex numbers Z₁ and Z₂ are defined as follows: ²1 i sin (2T)) ²₂ = 3 (cos(8) + i sin(8)) ²1 in polar form, where Z = IZ] (cos(0) + i sin(0)) 2₂ = Calculate |Z| = 0 = O-2π/3 a = + 9 (cos(2) b= 02π/3 OTT/3 O-π/3 08 Calculate Z in rectangular form, where Z= a + b i: Write your answers to 2 decin places O-TI

2Q: Express the complex number z=-2/4 +7i in polar form and also represent it graphically. Hence find the value of In(z).

Use DeMoivre’s Theorem to find z4 if z = 2 (cos 3π/4 + i sin 3π/4). Write your answer in standard form.

Derive the formula for the cos-1(z), where z is a complex number.

Can you correct what I did wrong in part a?

please explain with solution!

Find the four fourth roots of z= cos 4p/3 i+ sin 4p/3 . Leave your answers in trigonomet-ric form.

Please solve this problem

3. Let w = 3-3i and z=-2 +2√3i. (a) Express w and 2 in polar exponential form. (b) Express (wz) 10 in polar exponential form using the principal argument.