Complex Numbers in Exponential Form

​Are you ready for the post-class quiz?

By Valerie Loh

Complex Numbers in Exponential Form
De Moivre's Theorem

​Let's begin with an appertizer.

Multiple Choice

Which of the following is the conjugate of $$z=8e^{-j1.2}$$ ?

• $$-8e^{-j1.2}$$

• $$-8e^{j1.2}$$

• $$8e^{j1.2}$$

Explanation:
To find the conjugate of z in exponential form, the only part we change is the sign of the argument.

​

​Ready for the main course?

Multiple Choice

A drone receives a direction signal, $$D_1=9e^{-j\frac{\pi}{2}}$$ . This will be compared with a reference signal, $$D_2=3e^{j\frac{\pi}{2}}$$ by $$\frac{D_1}{D_2}$$ . Identify the argument of the resulting signal.

• $$-\frac{\pi}{4}$$

• $$-\pi$$

• $$\pi$$

• $$\frac{3\pi}{2}$$

​You got this!

Multiple Choice

Which of the following is the correct exponential form for $$z=-j6$$ ?

• $$-6e^{\ j\frac{\pi}{2}}$$

• $$6e^{\ j\frac{\pi}{2}}$$

• $$-6e^{-\ j\frac{\pi}{2}}$$

• $$6e^{\ -j\frac{\pi}{2}}$$

​Did you get it right?

Here comes the last dish!

Multiple Select

Choose all the correct statements about $$z=\left(1+j\right)^4$$ .

• The modulus of z is 4.

• The modulus of z is 8.

• The argument of z is $$\frac{\pi}{2}$$ .

• The argument of z is $$\pi$$ .

You did it!