Question

5+2i/3+4i express complex numbers A +IB

Answer 1

Step-by-step explanation:

see the attachment......

Answer 2

Answer:

Required answer is $\frac{22}{25} - i\frac{14}{25}$

Step-by-step explanation:

Given,

$\frac{5 + 2i}{3 + 4i}$

Denominator of the given term is (3+4i) and numerator is (5+2i)

We are multiplying denominator and numerator by (3-4i)

So,

$\frac{(5 + 2i)(3 - 4i)}{(3 + 4i)(3 - 4i)} \\ = \frac{5 \times 3 - 5 \times 4i + 2i \times 3 - 2i \times 4i}{ {3}^{2} - {(4i)}^{2} } \\ = \frac{15 - 20i + 6i - 8 {i}^{2} }{9 - 16 {i}^{2} } \\ = \frac{15 - 20i + 6i + 8}{9 + 16} \\ = \frac{22 - 14i}{25} \\ = \frac{22}{25} - i\frac{14}{25}$

So, A+iB form of 5+2i/3+4i is $\frac{22}{25} - i\frac{14}{25}$

Here applied formulas,

${i}^{2} = - 1 \\ {x}^{2} - {y}^{2} = (x + y)(x - y)$

This is a problem of Complex number.

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