Question

If z is a complex number such that | z | = 4 and arg(z) = $\frac{5\pi}{6}$ then z is equal to

• A. –2$\sqrt{3}$ + 2i
• B. 2$\sqrt{3}$ + 2i
• C. 2$\sqrt{3}$ – 2i
• D. – $\sqrt{3}$ + i

Answer 1

Answer: (A)

–2$\sqrt{3}$ + 2i

Answer 2

Sol. z = 1 = 1 (cos (arg(z) + i sin (arg(z))

= 4$\left( \cos\frac{5\pi}{6} + i\sin\frac{5\pi}{6} \right)$

= – 2$\sqrt{3}$ + 2i