AS 91577 · 2023 paper · a remainder, an unknown from a quotient, a surd equation, comparing parts, and a pair of conditions
Question 3(b) Achieved
Practises Equations, arguments, and comparing components
Five separate parts: a remainder, an unknown found from a quotient, an equation with two square roots, two unknowns found from a reciprocal, and a constant pinned down by two conditions at once.
The complex numbers u and v are u = n − i and v = 2 − 3i.
Given that u/v = 3 + 4i, find the value of n.
Work it out
Try it on paper first. Stuck? Take one hint at a time.
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1 Cross-multiply rather than dividing: u = v(3 + 4i).
n − i = (2 − 3i)(3 + 4i) -
2 Expand the right side.
6 + 8i − 9i − 12i2 = 18 − i -
3 Compare with n − i.
The imaginary parts already match (−1 each), and the real parts give n = 18.
What the marker wanted
- Achieved The value of n.
In our words, from NZQA’s 2023 marking schedule.
How did it go?
Got it moves it further out. Review brings it back tomorrow.