Question

If a complex number z lies on a circle of radius 12, then the complex number (1+4z) lies on a circle of radius.

Answer 1

Distance of the point representing z from the centre of the circle is |z−(−4+i0)|=|z+4|.

According to given condition |z+4|≤3

Now |z+1|=|z+4−3|≤|z+4|+|(−3)|≤3+3=6

Therefore , the greatest value of |z+1|is 6

Since least value of the modulus value of a complex number is zero , the least value of |z+1|=0.

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