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Maths Complex Number The Modulus and the Conjugate of a Complex Number Subjective Type

Published on: August 11, 2026

Let a, b be real and |Z 1 | ≠ b. Find |Z 2 | if = 1.

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The correct answer is:

CHECK THE SOLUTION.

Sol. = 1 implies . = 1

i.e. (aZ 1 – bZ 2 ) (a – b ) = (ab – Z 1 ) (ab – Z 2 )

i.e. |Z 1 | 2 |Z 2 | 2 – a 2 |Z 1 | 2 – b 2 |Z 2 | 2 + a 2 b 2 = 0

i.e. (|Z 1 | 2 –b 2 ) (|Z 2 | 2 –a 2 ) = 0 giving |Z 2 | = |a|

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