Question

The modulus and amplitude of 4 + 3i are ______

Options

• `5, tan^-1(3/4)`

• `sqrt7, tan^-1(3/4)`

• `sqrt7, tan^-1(4/3)`

• `5, tan^-1(4/3)`

Answer 1

The modulus and amplitude of 4 + 3i are `underline(5, tan^-1(3/4))`.

Explanation:

|z| = `sqrt(a^2 + b^2) = sqrt25 = 5`

Let θ be the argument of z.

∴ tanθ = `|b/a| = |3/4| = 3/4`

⇒ θ = `tan^-1(3/4)`