Question

what is the modulus of 5+4i

Answer 1

Answer:

$\boxed{\sf{Modulus \to \sqrt{41}}}$

Step-by-step explanation:

Concept used:

Let z = x + iy

Then, modulus of z = |z| = $\sqrt{x^{2}+y^{2}}$

Solution:

According to the question,

• x = 5
• y = 4

So, the modulus of z would be:

$\implies \sf{|z|=\sqrt{x^{2}+y^{2}}}$

$\implies \sf{|z|=\sqrt{5^{2}+4^{2}}}$

$\implies \sf{|z| = \sqrt{25+16}}$

$\implies \sf{|z|=\sqrt{41}}$

∴ Modulus of 5 + 4i = √41

Answer 2

Answer:

Answer:

$\begin{gathered}\boxed{\sf{Modulus \to \sqrt{41}}}\\\\\end{gathered}$

Step-by-step explanation:

Concept used:

Let z = x + iy

Then, modulus of z = |z| =

$\sqrt{x^{2}+y^{2}}$

$\begin{gathered}\\\end{gathered}$

Solution:

According to the question,

•x = 5

•y = 4

$\begin{gathered}\\\end{gathered}$

So, the modulus of z would be:

$\begin{gathered}\implies \sf{|z|=\sqrt{x^{2}+y^{2}}}\\\\\end{gathered}$

$\begin{gathered}\implies \sf{|z|=\sqrt{5^{2}+4^{2}}}\\\\\end{gathered}$

$\begin{gathered}\implies \sf{|z| = \sqrt{25+16}}\\\\\end{gathered}$

$\begin{gathered}\implies \sf{|z|=\sqrt{41}}\\\\\end{gathered}$

∴ Modulus of 5 + 4i = √41