Question

HELP!!!!

Which of the following is the absolute value of 6 − 3i?

A) 3i√3

B) 3√5

C) 3√5i

D) 3√3

Answer 1

B

Explanation:

We want to find the value of:

`\displaystyle |6-3i|`

Recall that given a complex number z in the form:

`z=a+bi`

The absolute value of z will be given by:

`\displaystyle |z| = √(a^2+b^2)`

We have the complex number:

`6-3i`

Thus, a = 6 and b = -3.

Then its absolute value will be:

`|6-3i|=√((6)^2+(-3)^2)`

Evaluate:

`\displaystyle |6-3i|= √(36+9)=√(45)=3√(5)`

Hence, our answer is B.