Question

The modulus of (1+2i)(3-4i) / (4+3i)(2-3i) is _____

Answer 1

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Answer:

√5/13

Step-by-step explanation:

(1+2i)(3-4i)/(4+3i)(2-3i)

= 11+2i / 17-6i

conjugate the denominator

11+2i /17-6i × 17+6i/17+6i

= 175+100i/325

= 7+4i/13

therefore,

7/13 + 4/13i

modulus = √x^2 + y^2

= √(7/13)^2 + (4/13)^2

= √5/13

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Answer 2

SOLUTION

TO DETERMINE

The modulus of

$\displaystyle \sf{ \frac{(1 + 2i)(3 - 4i)}{(4 + 3i)(2 - 3i)} }$

EVALUATION

Here the given complex number is

$\displaystyle \sf{ \frac{(1 + 2i)(3 - 4i)}{(4 + 3i)(2 - 3i)} }$

The required modulus

$\displaystyle \sf{ = \bigg| \frac{(1 + 2i)(3 - 4i)}{(4 + 3i)(2 - 3i)} \bigg| }$

$\displaystyle \sf{ = \frac{ | 1 + 2i | \: | 3 - 4i| }{ | 4 + 3i | \: | 2 - 3i | } }$

$\displaystyle \sf{ = \frac{ \sqrt{ {1}^{2} + {2}^{2} } \: \: \sqrt{ {3}^{2} + {( - 4)}^{2} } }{\sqrt{ {4}^{2} + {3}^{2} } \: \: \sqrt{ {2}^{2} + {( - 3)}^{2} }} }$

$\displaystyle \sf{ = \frac{ \sqrt{5} \times 5}{5 \times \sqrt{13} } }$

$\displaystyle \sf{ = \frac{ \sqrt{5} }{ \sqrt{13} } }$

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