$If z_{1} = 2 + i, z_{2} = 3 - i, z_{3} = - 5 + 2 i, z_{4} = - 6 - 4 i,$ then $z_{1} + z_{2} + z_{3} + z_{4}$ lies in which quadrant ?

Third

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Fourth

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First

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Second

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Solution

The correct option is A Third
$Given: z_{1} = 2 + i, z_{2} = 3 - i, z_{3} = - 5 + 2 i, z_{4} = - 6 - 4 i$
$\Rightarrow z_{1} + z_{2} + z_{3} + z_{4} = (2 + 3 - 5 - 6) + i (1 - 1 + 2 - 4)$
$\Rightarrow - 6 - 2 i$
Here both the real part and the imaginary part are negative.
$∴ z$ lies on the third quadrant.

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If z1=2+i, z2=3−i, z3=−5+2i, z4=−6−4i, then z1+z2+z3+z4 lies in which quadrant ?

The correct option is A ThirdGiven: z1=2+i, z2=3−i, z3=−5+2i, z4=−6−4i ⇒z1+z2+z3+z4=(2+3−5−6)+i(1−1+2−4) ⇒−6−2i Here both the real part and the imaginary part are negative. ∴ z lies on the third quadrant.

$If z_{1} = 2 + i, z_{2} = 3 - i, z_{3} = - 5 + 2 i, z_{4} = - 6 - 4 i,$ then $z_{1} + z_{2} + z_{3} + z_{4}$ lies in which quadrant ?