Question

what is the modulus of (1+4i)?​

Answer 1

Answer:

Let z = x + iy where x and y are real and i = √-1. Then the non negative square root of (x2+ y 2) is called the modulus or absolute value of z (or x + iy).

Modulus of a complex number z = x + iy, denoted by mod(z) or |z| or |x + iy|, is defined as |z|[or mod z or |x + iy|] = + x2+y2−−−−−−√ ,where a = Re(z), b = Im(z)

i.e., + Re(z)2+Im(z)2−−−−−−−−−−−−−√

Sometimes, |z| is called absolute value of z. Clearly, |z| ≥ 0 for all zϵ C.

For example:

(i) If z = 6 + 8i then |z| = 62+82−−−−−−√ = √100 = 10.

(ii) If z = -6 + 8i then |z| = (−6)2+82−−−−−−−−−√ = √100 = 10.

Answer 2

ANSWER

MODULAS OF THIS VECTOR IS MAGNITUDE

WHICH IS GIVEN BY

√ ( 1+(4)^2)

=√17

because position vector is from orgin and magnitude is distance apply distance formula

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