Question
Question: If iz<sup>3</sup> + z<sup>2</sup> – z + i = 0, then \| z \| equals –...
If iz3 + z2 – z + i = 0, then | z | equals –
A
4
B
1
C
3
D
None of these
Answer
1
Explanation
Solution
Sol. i{\overset{̶}{Z}}^{3} + {\overset{̶}{Z}}^{2} = \overset{̶}{Z}–i Ž {\overset{̶}{Z}}^{2}(i\overset{̶}{Z} + 1) = \overset{̶}{Z} – i
Ž i {\overset{̶}{Z}}^{2} (\overset{̶}{Z}–i) = (\overset{̶}{Z}–i)
\overset{̶}{Z}–i = 0 i{\overset{̶}{Z}}^{2} = 1
|\overset{̶}{Z}| = 1 |\overset{̶}{Z}| = 1