Mini Lecture

1. Find \(x\) and \(y\) if \((5x+2)-7i=4+(2y+1)i\).

2. Simplify: \([(3+2i)-(6+i)]+(5+i)\).

3. Simplify: \(i^{32}\) and \(i^{33}\).

4. Expand and simplify: \((3+2i)^2\)

5. Divide \(\displaystyle\frac{2i}{3+i}\).

Graph each complex number: \(2+4i\), \(-2-4i\), and \(2-4i\).

Graph the complex numbers \(1\), \(i\), \(-1\), and \(-i\).

Find the modulus of each of the complex numbers \(5i\), \(7\), and \(3+4i\).

Write \(z=-1+i\) in trigonometric form.

Mini Lecture

1. Write \(-1+i\) in trigonometric form.

2. Write \(2(\cos30^\circ+i\sin30^\circ)\) in standard form.

3. Write \(\cos210^\circ+i\sin210^\circ\) in standard form.

4. Write \(8i\) in trigonometric form.

5. Write \(3+4i\) in trigonometric form.

Find the product of \(z_1=1+i\sqrt{3}\) and \(z_2=-\sqrt{3}+i\) in standard form, and then write \(z_1\) and \(z_2\) in trigonometric form and find their product again.

Find \((1+i)^{10}\).

Find the quotient when \(20(\cos75^\circ+i\sin75^\circ)\) is divided by \(4(\cos40^\circ+i\sin40^\circ)\).

Divide \(z_1=1+i\sqrt{3}\) by \(z_2=\sqrt{3}+i\) and leave the answer in standard form. Then change each to trigonometric form and divide again.

Mini Lecture

1. Multiply: \(7(\cos110^\circ+i\sin110^\circ)\) and \(8(\cos47^\circ+i\sin47^\circ)\)

2. Divide: \(18(\cos51^\circ+i\sin51^\circ)\) by \(12(\cos32^\circ+i\sin32^\circ)\)

3. Simplify \((-\sqrt{3}+i)^4\)

Find the \(4\) fourth roots of \(z=16(\cos60^\circ+i\sin60^\circ)\).

Solve \(x^3+1=0\).

Solve the equation \(x^4-2\sqrt{3}x^2+4=0\).

Mini Lecture

1. Find \(3\) cube roots of \(8\).

2. Find \(4\) fourth roots for \(16(\cos120^\circ+i\sin120^\circ)\)

Graph the points \((3, 45^\circ)\), \(\left(2, -\displaystyle\frac{4\pi}{3}\right)\), \(\left(-4,\displaystyle\frac{\pi}{3}\right)\), and \((-5,-210^\circ)\) on a polar coordinate system.

Give three ordered pairs that name the same point as \((3,60^\circ)\).

Convert to rectangular coordinates.

1. \((4,30^\circ)\)

2. \(\left(-\sqrt{2},\displaystyle\frac{3\pi}{4}\right)\)

3. \((3,270^\circ)\)

Convert to polar coordinates.

1. \((3,3)\)

2. \((-2,0)\)

3. \((-1,\sqrt{3})\)

Change \(r^2=9\sin2\theta\) to rectangular coordinates.

Change \(x+y=4\) to polar coordinates.

Mini Lecture

1. Graph in polar coordinates.

   1. \((2,135^\circ)\)

   2. \((1,-135^\circ)\)

   3. \((-2.5,45^\circ)\)

2. What ordered pairs name the same point as \((2,60^\circ)\)?

3. Convert \((\sqrt{2}, -135^\circ)\) to rectangular coordinates.

4. Convert \((-2\sqrt{3}, 2)\) to polar coordinates.

Sketch the graph of \(r=6\sin\theta\).

Mini Lecture
Graph in polar coordinates.

1. \(r=3\)

2. \(\theta=45^\circ\)

3. \(r=3\sin\theta\)

4. \(r=2+2\sin\theta\)