If $z = 2 - 3i$, then show that $z^2 - 4z + 13 = 0$.

If z = 2 - 3i, then show that z² - 4z + 13 = 0. – Class 12 Mathematics

Question 4 of 19

z = 2 - 3i

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Direct substitution of $z=2-3i$ into $z^2-4z+13$ simplifies to $0$ .

Step 1 — Compute $z^2$ .

$z^2=(2-3i)^2 = 4 - 12i + 9i^2 = 4-12i-9 = -5-12i$ (using $i^2=-1$ ).

Step 2 — Compute $4z$ .

$4z = 4(2-3i) = 8-12i$ .

Step 3 — Combine. …