Question

Modulus and amplitude of(2+i)(3+i)

Answer 1

Answer:

(2+i)(3+i)

= 5 + 5i

So,

Modulus = 5√2

and,

Amplitude = tan^-1 (5/5)= tan^-1(1) = π/4

radians

Answer 2

Answer:

Let z = x + iy where x and y are real numbers and i = √(-1). Then the non-negative square root of (x2 + y2) is known as the modulus or absolute value of z. Modulus or absolute value of z is denoted by |z| and read as mod z.

Hence if z = x + iy, then |z| = |x+iy| = +√x2 + y2.

For example, if z = -3 + 4i then, |z| = |-3 + 4i |= √(-3)2 + 42 = 5.