If iz 3- z 2- z - i -0- then -z- equalsA- 4B- 3C- 2D- 1

The correct option is D 1 We can write the given equation as z^3+1/iz^2 1/iz+1=0 or z^3 iz^2+iz i^2=0 ⇒ z^2(z i)+i(z i)=0 ⇒ (z^2+i)(z i)=0 ⇒ z^2= i, z=i ⇒ |z| ...

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Byju's Answer

Standard XI

Mathematics

Modulus of a Complex Number

If iz 3+ z 2-...

Question

If $i z^{3} + z^{2} - z + i = 0$ , then $| z |$ equals

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Solution

The correct option is D
1

We can write the given equation as
$z^{3} + \frac{1}{i} z^{2} - \frac{1}{i} z + 1 = 0$
$or z^{3} - i z^{2} + i z - i^{2} = 0 \Rightarrow z^{2} (z - i) + i (z - i) = 0 \Rightarrow (z^{2} + i) (z - i) = 0 \Rightarrow z^{2} = - i, z = i \Rightarrow | z |^{2} = | - i | and | z | = | i | \Rightarrow | z |^{2} = 1 and | z | = 1 \Rightarrow | z | = 1$

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If iz3+z2−z+i=0, then |z| equals

The correct option is D 1 We can write the given equation as z3+1iz2−1iz+1=0 or z3−iz2+iz−i2=0⇒z2(z−i)+i(z−i)=0⇒(z2+i)(z−i)=0⇒z2=−i,z=i⇒|z|2=|−i| and |z|=|i|⇒|z|2=1 and |z|=1⇒|z|=1

If $i z^{3} + z^{2} - z + i = 0$ , then $| z |$ equals