- #1
cdummie
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Homework Statement
Of all complex numbers that fit requirement: ## |z-25i| \leq 15## find the one with the lowest argument.
Homework Equations
The Attempt at a Solution
z=a + ib (a, b are real numbers)
## \sqrt{a^2 + (b-25)^2} \leq 15 \\ a^2 + (b-25)^2 \leq 225 ##
The lowest possible argument is zero, in that case, complex number has only real part, which means that imaginary part is zero, it is obvious that none of the numbers with such argument fit this requirement, because, if b is zero then on the LHS we have a squared plus 625, which is way greater than 225 even without a^2.