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Further complex numbers — Question 185

Original QCE Vault practice · 7 marks

Q185 · Practice questionTechnology-freeComplex unfamiliar7 marks

QUESTION 185 (7 marks)

A game map has triangular zone with complex coordinates 0,2,2i0,2,2i. A portal transforms coordinates by w=(1+i)z+(2−i)w=(1+i)z+(2-i).
Original triangle O=(0,0), A=(2,0), B=(0,2). Equal scales.
a)
Determine the three transformed vertices.
[2 marks]
b)
Determine the transformed area and explain the change in area.
[2 marks]
c)
Write the transformation as (Re⁡wIm⁡w)=A(Re⁡zIm⁡z)+b\binom{\operatorname{Re}w}{\operatorname{Im}w}=A\binom{\operatorname{Re}z}{\operatorname{Im}z}+\mathbf b. Determine AA and b\mathbf b, and use the determinant to check your area scale factor.
[3 marks]
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