Express the following complex number in polar form and exponential for

1.	Express the following complex number in polar form and exponential form. -i
Answer» Let z = -i = 0 – i a = 0, b = -1 z lies on negative imaginary Y-axis. \|z\| = r = \(\sqrt{a^2+b^2}=\sqrt{0^2+(-1)^2}=1\) and θ = amp z = 270° = \(\frac{3\pi}2\) The polar form of z = r (cos θ + i sin θ) = 1 (cos 270° + i sin 270°) = 1\((cos\frac{3\pi}2+i sin\frac{3\pi}2)\) The exponential form of z = re^iθ = e^{\(\frac{3\pi}2i\)}

Express the following complex number in polar form and exponential form. -i

Answer»

Let z = -i = 0 – i

a = 0, b = -1

z lies on negative imaginary Y-axis.

|z| = r = \(\sqrt{a^2+b^2}=\sqrt{0^2+(-1)^2}=1\) and

θ = amp z = 270° = \(\frac{3\pi}2\)

The polar form of z = r (cos θ + i sin θ)

= 1 (cos 270° + i sin 270°)

= 1\((cos\frac{3\pi}2+i sin\frac{3\pi}2)\)

The exponential form of z = re^iθ = e^{\(\frac{3\pi}2i\)}