Algebra Question - Please Help

[Naeema F]

If z = -2i (√3 - 2i)

I have calculated z to be z = -4 - 2√3 i
and the modulus of z to be z-bar = -4 + 2√3 i

I have also calculated z in polar form with principal argument (attached in the image below). Could someone please verify if my answers are correct? Much appreciated.

 

[pka]

Your work is correct.

 

[HallsofIvy]

If z = -2i (√3 - 2i)

I have calculated z to be z = -4 - 2√3 i
and the modulus of z to be z-bar = -4 + 2√3 i

The "modulus" of a complex number is a real number, here \(\displaystyle \sqrt{16+ 12}= \sqrt{28}= 2\sqrt{7}\). \(\displaystyle -4+ 2\sqrt{3} i\) is the "complex conjugate" of z.

I have also calculated z in polar form with principal argument (attached in the image below). Could someone please verify if my answers are correct? Much appreciated.View attachment 22147