Question

Describe the region determined by the relation ∣z+I∣+∣z−i∣≤3:

a) ˚le
b) Ellipse
c) Triangle
d) Square

Answer 1

The region determined by the relation ∣z+I∣+∣z−i∣≤3 is a circle.

Step-by-step explanation:

The region determined by the relation ∣z+I∣+∣z−i∣≤3 is a circle.

Let's break down the given expression. The absolute value of a complex number z1 is given by ∣z1∣=√(x1²+y1²), where x1 and y1 are the real and imaginary parts of z1.

Therefore, ∣z+I∣=√((x+1)²+y²) and ∣z−i∣=√(x²+(y-1)²).

Now, the given inequality becomes √((x+1)²+y²)+√(x²+(y-1)²)≤3. This represents a circle with center (-1, 1) and radius 3. Hence, the correct answer is b) Circle.