The complex number $u=\dfrac{5+4i}{3-2i}$ . Express $u$ in the form $x+iy$ .

Model answer

7/13+22/13i

Also accepted: 0.54+1.69i, 7/13 + (22/13)i

Explanation:

u=\dfrac{5+4i}{3-2i}\times\dfrac{3+2i}{3+2i}=\dfrac{7+22i}{13}=\dfrac7{13}+\dfrac{22}{13}i

Derived from ZIMSEC Pure Mathematics Paper 2, November 2025, Q4

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