IB Mathematics Applications & Interpretation Topic…

In a signal model, the complex amplitude is $w=3\sqrt{3}-3\text{i}$ . The voltage at time $t$ is $V(t)=\Re\left(we^{3\text{i}t}\right)$ .

Express $w$ in the form $r\text{e}^{\text{i}\theta}$ .

Determine in the form .

Find the polar form of $z = 1 + i\sqrt{3}$

Consider $w = 2\left(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}\right)$ . The points represented on an Argand diagram by and form the vertices of a quadrilateral, .

Let $z=-\sqrt{3}+i$ , where the point representing lies in the second quadrant of the Argand diagram and angles are measured in radians.

Consider the complex numbers $z_1 = 1 + \sqrt{3}i$ , and .

Find the polar form of $w = 2 - 2i$

Find the polar form of $z \cdot w$

Find the polar form of $\frac{w}{z}$

Express $w^2$ and $w^3$ in modulus-argument form.

Sketch on an Argand diagram the points represented by $w^0$ , $w^1$ , $w^2$ and $w^3$ .

Show that the area of the quadrilateral $Q$ is $\frac{21\sqrt{3}}{2}$ .

Let $z = 2(\cos\frac{\pi}{n} + i\sin\frac{\pi}{n})$ , . The points represented on an Argand diagram by form the vertices of a polygon .

Find the modulus and argument of $z$ , and write $z$ in the form $r(\cos\theta+i\sin\theta)$ .

Hence find $z^3$ in Cartesian form.

Calculate the modulus of $w$ .

Calculate the argument of $w$ .

Find the smallest positive integer value of $n$ such that $w^n$ is a real number.

IB Mathematics Applications & Interpretation AHL 1.13—complex Numbers Continued Questionbank

IB Mathematics Applications & Interpretation AHL 1.13—complex Numbers Continued Questionbank

IB Mathematics Applications & Interpretation AHL 1.13—complex Numbers Continued Questionbank

IB Mathematics Applications & Interpretation AHL 1.13—complex Numbers Continued Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 1.13—complex Numbers Continued Questionbank