Maharashtra State BoardHSC Science (Electronics) 11th
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Find the modulus and amplitude of the following complex numbers. −8 + 15i - Mathematics and Statistics

Sum

Find the modulus and amplitude of the following complex numbers.

−8 + 15i

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Solution

Let z = −8 + 15i

Here a = −8 , b = 15

∴ |z| = `sqrt("a"^2 + "b"^2)`

= `sqrt((-8)^2 + 15^2`

= `sqrt(64 + 225)`

= `sqrt(289)`

= 17

The amplitude z is given by

θ = `pi + tan^-1("a"/"b")`

= `tan^-1(15/(-8)) + pi`

= `-tan^-1(15/8) + pi`   ...[∵ tan–1(– θ) = – tan–1θ]

Hence, modulus = 17 and 

amplitude = `-tan^-1(15/8)`

  Is there an error in this question or solution?
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