Complex Numbers and Compass Bearings

The video tutorial explains the arithmetic of multiplying complex numbers by the imaginary unit i, demonstrating how this operation results in rotations on the complex plane. It covers plotting these numbers and visualizing the rotations as 90-degree turns. The tutorial also compares this concept to compass bearings and unit circle rotations, highlighting the anti-clockwise direction of angle measurement in mathematics.

What is the result of multiplying a complex number by i?

• It doubles the magnitude of the number.

• It rotates the number 90 degrees anti-clockwise.

• It halves the magnitude of the number.

• It rotates the number 90 degrees clockwise.

What is the real part of the complex number obtained by multiplying 3i + i²?

• -3

• 3

• -1

• 1

After multiplying by i again, what is the real part of the resulting complex number?

• -1

• 1

• -3

• 3

What is the imaginary part of the complex number z4?

• 3i

• -3i

• i

• -i

What happens to the complex number when plotted on a graph after multiplying by i?

• It moves to the right.

• It moves to the left.

• It rotates 90 degrees anti-clockwise.

• It rotates 90 degrees clockwise.

Why is multiplying by i considered a boring choice for a common ratio?

• It results in a zero magnitude.

• It results in a negative magnitude.

• It results in a predictable rotation.

• It results in a constant magnitude.

What is the effect of multiplying a complex number by i on its position?

• It moves the number to the origin.

• It reflects the number across the x-axis.

• It rotates the number 90 degrees anti-clockwise.

• It rotates the number 180 degrees.

In compass bearings, from which direction do we start counting?

• West

• North

• East

• South

Why do we count clockwise in compass bearings?

• Because it is a historical convention.

• Because clocks count in that direction.

• Because it is the opposite of mathematical conventions.

• Because it is easier to calculate.

What would happen if we counted anti-clockwise in compass bearings?

• It would align with mathematical conventions.

• It would make navigation easier.

• It would have no effect.

• It would confuse the compass readings.