Convert each point from rectangular form to polar form:
a. (-1,1)
b. (-3,4)
a. (-1,1)
b. (-3,4)
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a. (-1,1) responds to -1 + i. First we find the magnitude:
|-1 + i| = √(1+1) = √2
√2(-1/√2 + i/√2)
The angle x where cosx = -1/√2 and sinx = 1/√2 is 3π/4. Hence it is written as:
√2(cos(3π/4) + isin(3π/4))=
√2 * ℮^(3πi/4)
b) We follow the same procedure.
(-3,4) responds to -3 + 4i and we find the magnitude:
|-3 + 4i| = √(9+16) = √25 = 5
5(-3/5 + 4i/5)
Using a calculator we find that the angle x that cosx = -3/5 and sinx = 4/5 is 2.215. Hence:
-3 + 4i = 5 * e^(2.215i)
|-1 + i| = √(1+1) = √2
√2(-1/√2 + i/√2)
The angle x where cosx = -1/√2 and sinx = 1/√2 is 3π/4. Hence it is written as:
√2(cos(3π/4) + isin(3π/4))=
√2 * ℮^(3πi/4)
b) We follow the same procedure.
(-3,4) responds to -3 + 4i and we find the magnitude:
|-3 + 4i| = √(9+16) = √25 = 5
5(-3/5 + 4i/5)
Using a calculator we find that the angle x that cosx = -3/5 and sinx = 4/5 is 2.215. Hence:
-3 + 4i = 5 * e^(2.215i)