Transformations from the z-plane to the w-plane

Transformations from the z-plane to the w-plane Quiz

Spec 4.2 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. The transformation w=2z+iw=2z+i maps z=3−iz=3-i to which point?

    • A. 6+i6+i
    • B. 6−i6-i
    • C. 5−i5-i
    • D. 6−3i6-3i

  2. 2. Under w=z2w=z^2, the half-line arg⁡z=π6\arg z=\frac{\pi}{6} is mapped to which half-line?

    • A. arg⁡w=π12\arg w=\frac{\pi}{12}
    • B. arg⁡w=π6\arg w=\frac{\pi}{6}
    • C. arg⁡w=π3\arg w=\frac{\pi}{3}
    • D. arg⁡w=π2\arg w=\frac{\pi}{2}

  3. 3. Find the image of z=2+iz=2+i under w=z2w=z^2.

    • A. 3+4i3+4i
    • B. 4+i4+i
    • C. 5+4i5+4i
    • D. 3+2i3+2i

  4. 4. Under w=1zw=\frac1z, the circle ∣z∣=4|z|=4 maps to

    • A. ∣w∣=4|w|=4
    • B. ∣w∣=14|w|=\frac14
    • C. ∣w∣=16|w|=16
    • D. ∣w∣=116|w|=\frac{1}{16}

  5. 5. Under w=1zw=\frac1z, the line y=xy=x maps to

    • A. u2+v2=1u^2+v^2=1
    • B. v=uv=u
    • C. u=0u=0
    • D. v=−uv=-u

Quiz