Q46 of 66 Page 91

If z is a complex number, then

Given z is a complex number.


Let z = x + yi


⇒ |z| = |x + yi| and |z|2 = |x + yi|2


⇒ |z|2 = x2 + y2 … (1)


Now z2 = x2 + y2i2 + 2xyi


⇒ z2 = x2 – y2 + 2xyi






So, |z|2 = x2 + y2 = |z|2


∴ |z|2 = |z2|

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