3+2i 2 5i + 3 2i 2+5i ( #10;3+2i ) ×( 2+5i ) +( 3 2i ) ( 2 5i #10; ) #160; 4 25( 1 ) #160; #10;6+15i+4i 10+6 15i 4i 10 29 = 12 20 ...

200

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Complex Numbers

3+2i2-5i+3-2i...

Question

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

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Solution

$\frac{3 + 2 i}{2 - 5 i} + \frac{3 - 2 i}{2 + 5 i}$
$\frac{(3 + 2 i) \times (2 + 5 i) + (3 - 2 i) (2 - 5 i)}{4 - 25 (- 1)}$
$\frac{6 + 15 i + 4 i - 10 + 6 - 15 i - 4 i - 10}{29} = \frac{12 - 20}{29} = \frac{- 8}{29}$

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\frac{3 + 2 i}{2 - 5 i} + \frac{3 - 2 i}{2 + 5 i}

\frac{3 + 2 i}{2 - 5 i} + \frac{3 - 2 i}{2 + 5 i}

z : z^{2} - (3 - 2 i) z = (5 i - 5)

z = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 + 2 i & - 5 i 1 - 2 i & - 3 & 5 + 3 i 5 i & 5 - 3 i & 7 \end{matrix} ∣ ∣ ∣ ∣

z = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 + 2 i & - 5 i 1 - 2 i & - 3 & 5 + 3 i 5 i & 5 - 3 i & 7 \end{matrix} ∣ ∣ ∣ ∣

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