Complex Number
Exercises for students
Solve the following problems on paper and check your answers using the above applet:
Given that z = 3 + 0.5i, find the modulus and argument of z
and write down the values of z*, -z and 1/z in the form a + ib.
Given that z = 0.5 + 1.2i, find the modulus and argument of z
and write down the values of iz, -z and -iz in the form a + ib.
Summary
If z = x + iy, then
| z* | = | conjugate of z | = | x - iy |
| -z | = | -(x + iy) | = | -x - iy |
| iz | = | i(x + iy) | = | -y + ix |
| -iz | = | -i(x + iy) | = | y - ix |
| 1/z | = | 1/(x + iy) | = | (x - iy)/(x2 + y2) |
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