Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Plot the complex number z=3−4iz = 3 - 4iz=3−4i on an Argand diagram.
Plot the points corresponding to z=2+iz=2+iz=2+i, −z-z−z, z‾\overline{z}z and −z‾-\overline{z}−z on an Argand diagram and describe the quadrilateral formed.
Given z1=2+3iz_{1}=2+3iz1=2+3i and z2=−1+2iz_{2}=-1+2iz2=−1+2i, plot the point representing z1+z2z_{1}+z_{2}z1+z2 on an Argand diagram.
Let z1=1+3iz_{1}=1+\sqrt{3}iz1=1+3i. Find the image of z1z_{1}z1 under multiplication by iii and plot both points on an Argand diagram.
Plot the complex number z=−3+4iz=-3+4iz=−3+4i and its reflection in the real axis on an Argand diagram.
Sketch the locus of points zzz in the Argand diagram satisfying Re(z)=−1\mathrm{Re}(z)=-1Re(z)=−1
For z=2+2iz=2+2iz=2+2i, plot zzz and 2z2z2z on the same Argand diagram.
Plot the complex number z=1−iz = 1 - iz=1−i and its image under multiplication by iii on an Argand diagram.
The vertices of a triangle in the Argand diagram are given by: z1=i,z2=2,z3=−1+2iz_{1}=i,\quad z_{2}=2,\quad z_{3}=-1+2iz1=i,z2=2,z3=−1+2i
Plot these points and determine the coordinates of the centroid on the diagram.
Plot the complex number z=1+2iz = 1 + 2iz=1+2i and its conjugate z‾\overline{z}z on an Argand diagram.
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Question Type 2: Multiplying by a conjugate
