- #1

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z = a + ib

z*z = (a - ib)(a + ib) = a^2 + b^2

z^2 = (a + ib)^2 = a^2 + 2iab - b^2

So it must have something to do with the absolute value, but I don't understand what or why.

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- Thread starter jaejoon89
- Start date

- #1

- 195

- 0

z = a + ib

z*z = (a - ib)(a + ib) = a^2 + b^2

z^2 = (a + ib)^2 = a^2 + 2iab - b^2

So it must have something to do with the absolute value, but I don't understand what or why.

- #2

- 311

- 1

|z| = sqrt(a^2 + b^2)

Geometrically it gives the distance of the complex number from the origin on the Argand Plane.

And quite obviously |z|^2 is NOT EQUAL TO z^2

- #3

Dick

Science Advisor

Homework Helper

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|z|^2 is conjugate(z)*z=a^2+b^2. It's not equal to z^2.

- #4

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- 0

- #5

Dick

Science Advisor

Homework Helper

- 26,263

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