IB Mathematics Analysis and Approaches Topic AHL…

Given the complex number $w = 5(\cos \frac{\pi}{4} + i\sin \frac{\pi}{4})$ .

Convert the complex number $w$ to its Cartesian form.

Plot the complex number $w$ on an Argand diagram.

The complex number $w$ is defined by $w = 2e^{i\frac{\pi}{4}}$ . Points , and on an Argand diagram represent the complex numbers , and respectively (where denotes the complex conjugate of ).

Consider the complex equation $z^4 = 256i$ , where $z \in \mathbb{C}$ . The equation has four distinct roots , which can be written in the form , with and .

Consider a complex number $z=-3+3i$ .

It is given that $w = \frac{2-i}{1+3i}$ .

the Argand diagram showing the points $A$ , $B$ and $C$ ,.

the area of triangle $ABC$ .

Find the values of $z_1, z_2, z_3$ and $z_4$ , expressing them in polar form.

These roots $z_1, z_2, z_3$ and form a geometric sequence.

On an Argand diagram, the roots are represented by points $A, B, C, D$ .

Plot the points $A, B, C$ and $D$ on an Argand diagram.

The equation $v^4 = a + bi$ ( $a, b \in \mathbb{R}$ ) has the complex conjugates as its roots.

Let $A', B', C', D'$ be the midpoints of the segments respectively. Consider the equation () for which the four points are roots.

Find the argument of $z$ in radians, expressing it to three significant figures.

Write $z$ in polar form $r\operatorname{cis}\theta$ .

Express $w$ in the form $x+iy$ .

Find the argument of $w$ , giving your answer in radians.

Find the modulus of $w$ , giving your answer in the form $a\sqrt{b}$ .

IB Mathematics Analysis and Approaches AHL 1.12—complex Numbers – Cartesian Form and Argand Diag Questionbank

IB Mathematics Analysis and Approaches AHL 1.12—complex Numbers – Cartesian Form and Argand Diag Questionbank

IB Mathematics Analysis and Approaches AHL 1.12—complex Numbers – Cartesian Form and Argand Diag Questionbank

IB Mathematics Analysis and Approaches AHL 1.12—complex Numbers – Cartesian Form and Argand Diag Questionbank

IB Mathematics Analysis and Approaches (AA) Topic AHL 1.12—complex Numbers – Cartesian Form and Argand Diag Questionbank