The value of -9- i 5- i -2-3 i 4-5 i - is

We know |Z_1/Z_2| = |Z_1|/|Z_2| ⇒ |(9+i)(5+i)/(2+3i)(4+5i)| = |(9+i)(5+i)|/|(2+3i)(4+5i)| |Z_1.Z_2| = |Z_1|.|Z_2| = |(9+i)||(5+i)|/|(2+3i)||(4+5i)| ⇒ √(82 ...

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Standard XII

Mathematics

Modulus of a Complex Number

The value of ...

Question

The value of | $\frac{(9 + i) (5 + i)}{(2 + 3 i) (4 + 5 i)}$ | is _________

_

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Solution

We know | $\frac{Z_{1}}{Z_{2}}$ | = $\frac{| Z_{1} |}{| Z_{2} |}$

⇒ | $\frac{(9 + i) (5 + i)}{(2 + 3 i) (4 + 5 i)}$ | = $\frac{| (9 + i) (5 + i) |}{| (2 + 3 i) (4 + 5 i) |}$

| $Z_{1}$ . $Z_{2}$ | = | $Z_{1}$ |.| $Z_{2}$ |

= $\frac{| (9 + i) | | (5 + i) |}{| (2 + 3 i) | | (4 + 5 i) |}$

⇒ $\frac{\sqrt []{82} \sqrt []{26}} {\sqrt []{13} \sqrt []{41}}$ = 2

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∣ ∣ ∣ ∣ ∣ \begin{matrix} - 5 & 3 + 5 i & \frac{3}{2} - 4 i 3 - 5 i & 8 & 4 + 5 i \frac{3}{2} + 4 i & 4 - 5 i & 9 \end{matrix} ∣ ∣ ∣ ∣ ∣

,
its value is

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a

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∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} - 7 & 5 + 3 i & \frac{2}{3} - 4 i 5 - 3 i & 8 & 4 + 5 i \frac{2}{3} + 4 i & 4 - 5 i & 9 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣

is real.

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The value of |(9+i)(5+i)(2+3i)(4+5i)| is ___________ ___

We know |Z1Z2| = |Z1||Z2| ⇒ |(9+i)(5+i)(2+3i)(4+5i)| = |(9+i)(5+i)||(2+3i)(4+5i)| |Z1.Z2| = |Z1|.|Z2| = |(9+i)||(5+i)||(2+3i)||(4+5i)| ⇒ \(\frac{\sqrt []{82} \sqrt []{26}} {\sqrt []{13} \sqrt []{41}}\) = 2

The value of | $\frac{(9 + i) (5 + i)}{(2 + 3 i) (4 + 5 i)}$ | is _________

_