how to do this question? (1 Viewer)

r25nd · Feb 5, 2025

idk why i'm not getting this? what to do i dooo

"On an Argand diagram, the points P and Q represent z1 and z2 respectively. OPQ is an equilateral triangle. Show that z1² + z2² = z1z2"

jimmysmith560 · Feb 5, 2025

Would the following working help?

liamkk112 · Feb 5, 2025

r25nd said:
idk why i'm not getting this? what to do i dooo

"On an Argand diagram, the points P and Q represent z1 and z2 respectively. OPQ is an equilateral triangle. Show that z1² + z2² = z1z2"

the sides are all equal. WLOG let z2 be the side that is a 60 degree counterclockwise rotation of z1. so then, z1 = z2cis60.
thus $z_1^2 + z_2^2 = z_2^2(1+(cis(60))^2) = z_2^2(1+cis(120)) =z_2^2(1-0.5+i\sin(120))=z_2^2(0.5+i\sin(60)) =z_2^2cis(60)$
$z_1z_2 = z_2^2cis(60) =z_1^2 + z_2^2$

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how to do this question? (1 Viewer)

r25nd

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jimmysmith560

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liamkk112

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