Complex Numbers Extension 2

 HSC complex numbers Extension 2 introduces a number system beyond the real line. Students work with z = a + bi, plot points on the Argand diagram, convert between Cartesian and modulus-argument form, and apply De Moivre's theorem to powers and roots.

Topics covered in the HSC

• Arithmetic of complex numbers — addition, multiplication, conjugates
• Modulus and argument; modulus-argument (polar) form
• Argand diagram geometry — loci, regions, and transformations
• De Moivre's theorem — finding powers and nth roots of complex numbers
• Connection to polynomials — complex roots and conjugate pairs

Revision resources

The HSC Complex Numbers booklet at Vu's Maths Hub provides algebra, geometry, and application problems with full worked solutions.

Complex numbers link directly to HSC Polynomials (roots in ℂ) and HSC Trigonometry (Euler's formula connections).

Exam tips

Always sketch the Argand diagram. Convert to modulus-argument form before applying De Moivre. Check that your roots are evenly spaced around a circle.

Extension 2 worked solutions, NESA-aligned content, and free HSC Maths booklets — everything at vumaths.com.