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

Monjur Alahi

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


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Salim Ahmed Kawsar

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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 = reiθ = e\(\frac{3\pi}2i\)

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