← Complex numbers: past papers

AS 91577 · 2023 paper · dividing in polar form, a modulus in k, an argument, cube roots, and a tangent to a circle

Question 2(a) Achieved

Practises Argand diagram & polar form

Five separate parts: a quotient of two numbers in polar form, the modulus of a difference, an argument found from an equation, the cube roots of a negative number, and a line that touches a circular locus.

If u = q6 cis(5π/8) and v = q2 cis(2π/5), write u/v in the form r cisθ.

The 2023 paper, page 5 ↗ Marking schedule, page 3 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

  1. 1 In polar form, how do you divide?

    Divide the moduli and subtract the arguments.

  2. 2 The moduli first.

    q6/q2 = q4

  3. 3 Now the arguments. Use a common denominator.

    5π/8 − 2π/5 = 25π/40 − 16π/40 = 9π/40
Answer u/v = q4 cis(9π/40)

What the marker wanted

  • Achieved The correct quotient in polar form.

In our words, from NZQA’s 2023 marking schedule.

How did it go?

Got it moves it further out. Review brings it back tomorrow.