Question

If z=4-3i, then |z| is

Answer 1

Answer:

4+3i

Step-by-step explanation:

|Z|=√4^2-3^2

=√16-9

=4√-9

=4+3

Answer 2

If $z=4-3i$, then the magnitude of z, $\lvert z \rvert$ equals 5.

Step-by-step Explanation

Given:

A complex number, $z=4-3i$

To be found:

To find the magnitude of z or $\lvert z \rvert$.

Solution:

The given complex number, $z=4-3i$ is of the standard form, $z=x+ iy$

$\implies x=4$ and $y=-3$

We know that the magnitude of z is given by the formula, $\lvert z \rvert=\sqrt{x^{2} +y^{2} }$

So, substituting the given values in the formula, we get

$\lvert z \rvert=\sqrt{4^{2} +(-3)^{2} }\\\implies \lvert z \rvert=\sqrt{16+9}\\\implies \lvert z \rvert=\sqrt{25}$

Simplifying, we get

$\lvert z \rvert=5$

Hence, $\lvert z \rvert$ is equal to 5 when $z=4-3i$.

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