SOLUTION: Hello, how do I figure out this complex numbers problem? Any help is greatly appreciated!
The point (-4+bi)has been plotted on the complex plane and r=8. If 0°≤θͰ
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Question 396764: Hello, how do I figure out this complex numbers problem? Any help is greatly appreciated!
The point (-4+bi)has been plotted on the complex plane and r=8. If 0°≤θ≤180° find the value of b. Leave answer as a radical.
Thank you.
Found 2 solutions by jsmallt9, richard1234:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The "a" and "b" in standard form and the "r" in polar form are related by the equation:
Subsituting the value we have for "a" and "r" we get:
Simplifying we get:
Subtracting 16 we get:
Now we find the square root of each side. Since the theta is between 0 and 180, we want "b" to be positive. (A negative "b" would put theta between 180 and 360.) So we will only use the positive square root:
All that is left is simplifying:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The magnitude of the complex number is . Simplifying,
. Note that b must be positive since the angle is between 0 and 180, so .
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