5+2i 1 i + 5 2i 1+i =a+ib ⇒ 5+5i+2i 2+5 5i 2i 2 1+1 =a+ib ⇒62=a+bi ⇒ 3=a+bi ⇒ a=3, #160; b=0 Hence, the answer is a= ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Algebra of Complex Numbers

5+2i 1-i + 5-...

Question

$\frac{5 + 2 i}{1 - i} + \frac{5 - 2 i}{1 + i}$

Open in App

Solution

$\frac{5 + 2 i}{1 - i} + \frac{5 - 2 i}{1 + i} = a + i b$
$\Rightarrow \frac{5 + 5 i + 2 i - 2 + 5 - 5 i - 2 i - 2}{1 + 1} = a + i b$
$\Rightarrow \frac{6}{2} = a + b i$
$\Rightarrow 3 = a + b i$
$\Rightarrow a = 3,$ $b = 0$
Hence, the answer is $a = 3, b = 0.$

Suggest Corrections

Similar questions

{(5 - 3 i)}^{3}

\frac{5 + \sqrt{2} i}{1 - \sqrt{2} i}

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

i = (\sqrt{- 1})

x = \frac{(3 + i \sqrt{5}) (3 - i \sqrt{5})}{(\sqrt{3} + \sqrt{2} i) - (\sqrt{3} - \sqrt{2} i)}

\infty \sum i = 1 \frac{2 i - 1}{2^{i + 1}}

\frac{1 - 2 i}{2 + i} + \frac{4 - i}{3 + 2 i} =

Join BYJU'S Learning Program