Question

Find the modulus of (2+3i)^2/-1+5i

Answer 1

Answer:

The required answer is $\sqrt{\frac{13}{2}}$

Step-by-step explanation:

Modulus: A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count.

The residue following division is also referred to as the modulus. For instance, if we divide $17$ by $5$, we obtain $3$ with a residual, therefore $17$mod $5 = 2$. Since analog clocks run on a modulus of $12$, or times past $12,$ they are frequently referred to as clock arithmetic.

Given: The given complex quantity is $\frac{(2+3i)^2}{-1+5i}$

To find: modulus.

We have

z= $\frac{(2+3i)^2}{-1+5i}$

$\Rightarrow|z|=\arrow|\frac{(2+3i)^2}{-1+5i}|$

$\Rightarrow|z|=\frac{\arrow|{(2+3i)^2}|}{\arrow|{-1+5i}|}$

$\Rightarrow|z|=\frac{\arrow|{2+3i}|^2}{\arrow|{-1+5i}|}$

$\Rightarrow|z|=\frac{(\sqrt{(2)^{2}+(-3)^{2}})}{(\sqrt{(-1)^{2}+(5)^{2}})}=\frac{(\sqrt{13})^{2}}{{\sqrt{26}}}=\frac{13}{\sqrt{26}}$

$\Rightarrow|z|=\sqrt{\frac{13}{2}}$

Therefore, the required modulus $\sqrt{\frac{13}{2}}$

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