9709 · topic questions
Complex numbers
12 past-paper questions on Complex numbers
Find the complex numbers z for which (z+4)/(z+4i) is real and |z|= √10. Give your answers in the form z = x+iy, where x and y are…
Practise the full question →The square roots of 24-7i can be expressed in the Cartesian form x+iy, where x and y are real and exact. By first forming a…
Practise the full question →On an Argand diagram shade the region whose points represent complex numbers z which satisfy both the inequalities |z-4-3i|<2 and…
Practise the full question →The square roots of 6-8i can be expressed in the Cartesian form x+iy, where x and y are real and exact. By first forming a…
Practise the full question →Find the complex number z satisfying the equation (z-3i)/(z+3i) = (2-9i)/5. Give your answer in the form x+ iy, where x and y are…
Practise the full question →The square roots of -1-4√5 i can be expressed in the Cartesian form x+iy, where x and y are real and exact. By first forming a…
Practise the full question →On an Argand diagram shade the region whose points represent complex numbers z which satisfy both the inequalities |z-3i|<2 and…
Practise the full question →Express z and ω in the form re^(iθ), where r > 0 and −π < θ ≤ π. Give the exact values of r and θ in each case.
Practise the full question →On a single Argand diagram sketch the loci given by the equations |z-3+2i|= 2 and |w-3+2i|=|w+3-4i| where z and w are complex…
Practise the full question →Show that (a-½)² +b² = ¼, where a and b are the functions of y found in part (a).
Practise the full question →On a single Argand diagram, sketch the loci given by the equations Re(z) = 1 and |z - ½| = ½. where z is a complex number.
Practise the full question →z = 3e^(πi/4) is a root of the equation z² + bz+ c = 0, where b and c are real. State the other root and hence find the values of…
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Complex numbers (9709) past-paper questions — marked instantly
These are real Cambridge Mathematics past-paper questions on Complex numbers. Open one, attempt it, then upload your working — MarkScheme grades it against the official 9709 mark scheme so you see exactly where the marks are won and lost on this topic.
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- This page collects 12 recent Cambridge Mathematics (9709) past-paper questions tagged to Complex numbers. Each links straight to instant marking against the official 9709 scheme.
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