Express the quotient in polar form with principal argument −π<θ≤π.

01 / Standard#Your turn

z=\frac{\sqrt3+i}{1+i}

Official paper · jm02-2024 · 4(a)(i) · PDF 6

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Find modulus and argument of numerator and denominator.

Hint 2

Divide moduli and subtract arguments.

Worked solution

Write the two numbers in polar form.
$\sqrt3+i=2\operatorname{cis}(\pi/6),\quad1+i=\sqrt2\operatorname{cis}(\pi/4)$
The resulting argument is already principal.
$z=\sqrt2[\cos(-\pi/12)+i\sin(-\pi/12)]$

Modulus √2, principal argument −π/12.

Checks and common pitfalls: Arguments subtract under division.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Write the two numbers in polar form.
$\sqrt3+i=2\operatorname{cis}(\pi/6),\quad1+i=\sqrt2\operatorname{cis}(\pi/4)$
The resulting argument is already principal.
$z=\sqrt2[\cos(-\pi/12)+i\sin(-\pi/12)]$

Think first. Reveal a hint when the class is ready.

2024 JM02