Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

Simplifying complex numbers

So according to my textbook
|iz*/2 - i/2| simplifies to |z-1|/2

where z* is the conjugate of z.

I can't work out how they got that so could someone please show it to me.
Thanks.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Simplifying complex numbers

hi mrpace

| iz*/2 - i/2 | = 1/2 . |z* - 1|

Say z = a + ib then z* = a - ib

z* - 1  = a - ib - 1 = (a-1) - ib

z - 1 = (a - 1) + ib

as the |    | is just root of real^2 + img^2 these are the same.

Bob

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Children are not defined by school ...........The Fonz
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zetafunc

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Registered: 2014-05-21

Posts: 2,436

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Re: Simplifying complex numbers

It now remains for you to show that

.