Maharashtra State BoardHSC Science (Electronics) 11th
Advertisement Remove all ads

Find the modulus and amplitude of the following complex numbers. −4 − 4i - Mathematics and Statistics

Sum

Find the modulus and amplitude of the following complex numbers.

−4 − 4i

Advertisement Remove all ads

Solution

Let z = −4 − 4i.

Here x = −4, y = −4

∴ |z| = `sqrt(x^2 + y^2)`

= `sqrt((-4)^2 + (-4)^2`

= `sqrt(16 + 16)`

= `sqrt(32)`

= `4sqrt(2)`

The amplitude θ is given by

θ = `tan^-1(y/x)`

= `tan^-1((-4)/(-4))`

= tan−1(1)

= `tan^-1(tan  pi/4)`

= `pi/4`

Hence, modulus = `4sqrt(2)` and 

amplitude = tan−1(1) or `(pi/4)`

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×