Question

Find the modulus and amplitude for following complex number:

7 - 5i

Answer 1

Let z = 7 – 5i

a = 7, b = -5

i.e. a > 0, b < 0

|z| = \(\sqrt{a^2+b^2}\) = \(\sqrt{7^2+(-5)^2}\)

 = \(\sqrt{49+25}\) = \(\sqrt{74}\)

Here, (7, -5) lies in 4th quadrant.