Question 21 of 28intermediate🔧 ApplyNumerical2 marks

Let z1=2−i,z2=−2+iz_1 = 2 - i, z_2 = -2 + i. Find (i) Re(z1z2zˉ1)\text{Re}\left( \frac{z_1 z_2}{\bar{z}_1} \right), (ii) Im(1z1zˉ1)\text{Im}\left( \frac{1}{z_1 \bar{z}_1} \right).

(i)
Answer

-25\frac{2}{5}

(ii)
Answer

0

Explanation

This question tests understanding of complex number operations including multiplication, division, conjugates, and modulus. Part (i) requires computing the product z₁z₂, then dividing by the conjugate of z₁. Part (ii) uses the fundamental property that z·z̄ = |z|², which simplifies the calculation significantly.

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