JEE Maths›Complex Numbers & Quadratic Equations›Visual Solution
Visual SolutionPYQ 2024Easy
Question
The conjugate of 2−3i2 - 3i is:
(A)−2+3i-2 + 3i
(B)2+3i2 + 3i
(C)−2−3i-2 - 3i
(D)3−2i3 - 2i
Solution Path
Conjugate flips sign of imaginary part: 2−3i‾=2+3i\overline{2 - 3i} = 2 + 3i.
01Question Setup
1/4
Find the conjugate of 2−3i2 - 3i.
2−3i‾=  ?\overline{2 - 3i} = \;?
02Conjugate Definition
2/4
a+bi‾=a−bi\overline{a + bi} = a - bi. Flip the sign of the imaginary part.
a+bi‾=a−bi\overline{a + bi} = a - bi
03ApplyKEY INSIGHT
3/4
z=2−3iz = 2 - 3i, so zˉ=2+3i\bar{z} = 2 + 3i.
zˉ=2+3i\bar{z} = 2 + 3i
04Final Answer
4/4
2−3i‾=2+3i\overline{2 - 3i} = 2 + 3i.
2+3i\boxed{2 + 3i}
Concepts from this question1 concepts unlocked
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Conjugate Symmetry on Argand Plane

STANDARD

Conjugate pairs are reflections across the real axis

z=x+iy  ⟹  zˉ=x−iyz = x + iy \implies \bar{z} = x - iy

Recognizing conjugate pairs halves the computation - products simplify dramatically

Locus problemsGeometric interpretationSymmetric root problems
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