Question

(3‐2i) (2+3i)/ (1+2i) (2‐i)​

Answer 1

Answer:

6 + 9i - 4i - 6i^2 / 2 -i + 4i - 2i^2.,, 6 + 5i +6 / 2 -i +3.,, 12 + 5i / 5- i

Answer 2

Step-by-step explanation:

TO FIND,

• Found the conjugate in given Equation

$\blue{ \underline{QUESTION \: : - }}$

$\huge{ \bold{ \frac{(3 - 2i) \: 2 + 3i}{(1 + 2i) \: (2 - i)}}}$

$\star{ \pink{ \underline{ \underline{Ｓｏｌｕｔｉｏｎ \: : - }}}}$

$\sf{ = \frac{6 + 9i - 4i - {6i}^{2} }{2 - i + 4i - {2i}^{2} }}$

$\sf{ = \frac{6 + 9i - 4i - 6 \times ( - 1)}{2 - i + 4i - 2 \times ( - 1)}}$

$\sf{ = \frac{ 6 + 9i - 4i + 6}{2 - i + 4i + 2}}$

$\sf{ = \frac{12 + 5i}{4 + 3i} \times \frac{4 - 3i}{4 - 3i}}$

$\sf{ = \frac{48 - 36i + 20i - {15i}^{2} }{ {4}^{2} - ({3i})^{2} }}$

$\sf{ \ = \frac{48 - 36i + 20i - {15i}^{2} }{16 - 3 \times ( - 1)}}$

$\sf{ = \frac{48 - 36i + 20i - 15 \times ( - 1)}{16 + 9}}$

$\sf{ \ = \frac{48 - 16i + 15}{25}}$

$\sf{ = \frac{63 - 16i}{25}}$

$\boxed{ \huge{ \purple{ \sf{a + ib}}}}$

Conjugate:-

$\sf{ = \frac{63}{25} - \frac{16}{25}i}$

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INFORMATION ABOUT IOTA➔

• i = √-1

• i²= -1

• i³ = -i

• i⁴ = 1

COMPLEX NUMBERS Formula➔

• Z = a +ib

a = REAL PART

b = IMAGINARY PART

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