rumbleroar
Survivor of the HSC
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q19 t-t
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Complex numbers question (1 Viewer)
- Thread starter rumbleroar
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q19 t-t
Kurosaki
True Fail Kid
What you do is draw the Argand diagram of the unit circle, and make in two arbitrary points to represent z and w.
Since they both have modulus one, when you draw the vector representing z+w, notice that this forms an isosceles triangle. Find the angle that is formed between the two equal sides of this triangle.
You can probably work from there.
Since they both have modulus one, when you draw the vector representing z+w, notice that this forms an isosceles triangle. Find the angle that is formed between the two equal sides of this triangle.
You can probably work from there.
rumbleroar
Survivor of the HSC
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Thank you 
First let z = cos@+isin@ and w = cos#+isin#
Then split the problem into two parts: one to find mod z+w and the other to find arg z+w
to find modulus, use |z| = sqrt(a^2+b^2)
to find argument, use arg(z) = tan-1(b/a)
also, to simplify cos@+cos# and sin@+sin#, you need to use the sum to product rules on http://math.ucsd.edu/~wgarner/math4c/textbook/chapter6/product_sum_formulas.htm (equation 5 and 7)
Then split the problem into two parts: one to find mod z+w and the other to find arg z+w
to find modulus, use |z| = sqrt(a^2+b^2)
to find argument, use arg(z) = tan-1(b/a)
also, to simplify cos@+cos# and sin@+sin#, you need to use the sum to product rules on http://math.ucsd.edu/~wgarner/math4c/textbook/chapter6/product_sum_formulas.htm (equation 5 and 7)