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# De Moivre's Theorem?

Hi! Need some help. I get that z1z2 must be along the terminal side of the angle (theta1+theta2) but how do I find the its length, that is, r1r2?

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- Φ² = Φ+1Lv 71 month ago
Construct the triangle with vertices 0, 1 and z₁.

Then construct the similar triangle 0, z₂, and z₁z₂.

|z₁z₂|=|z₁||z₂|

e.g. |3+4i|=5 and |5+12i|=13 so |(3+4i)(5+12i)|=5×13=65

Of course, it may be worthwhile knowing determining that (3+4i)(5+12i)=-33+56i.

- rotchmLv 71 month ago
Hint: State De Moivre's Theorem here. Then, un-anon yourself. Then, we will detail further.

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