Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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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  • 1 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.

  • rotchm
    Lv 7
    1 month ago

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

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