An algebra problem by Ojasvi Sharma

Algebra Level pending

The area (in sq. units) of the circle inscribed in the region denoted by |Re(z)|+|Im(z)| =10 equals to

50π 110π 55π 100π 130π

Ojasvi Sharma by Ojasvi Sharma , 19, India

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1 solution

Tom Engelsman
Sep 1, 2017

If z = a + b i z = a + bi , then the described region is just ∣ a ∣ + ∣ b ∣ = 10 |a| + |b| = 10 , or ∣ a ∣ − 10 ≤ b ≤ − ∣ a ∣ + 10. |a| - 10 \le b \le -|a| + 10. This is simply a square of side length 10 2 10\sqrt{2} , and the radius of the inscribed circle is just half this length. Therefore, the required area equals π ⋅ ( 5 2 ) 2 = 50 π . \pi \cdot (5\sqrt{2})^2 = \boxed{50\pi}.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

A perfect answer.😊

Ojasvi Sharma - 3 years, 9 months ago

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