If $A = - 1 - i, B = 2 + 3 i$ , then find length of AB

- 3 - 4 i

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1 + 2 i

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5

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(5)^{\frac{1}{2}}

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Solution

The correct option is B $5$
We know, length= $| z_{1} - z_{2} |$
$= | - 1 - i - (2 + 3 i) |$
$= | - 3 - 4 i |$
$= 5$
Ans: C

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Q. If

\frac{(1 + i) (2 + 3 i) (3 - 4 i)}{(2 - 3 i) (1 - i) (3 + 4 i)} = a + i b

, then

a^{2} + b^{2} =

Express the following complex numbers in the standard form a + i b :

$(i) (1 + i) (1 + 2 i) (i i) \frac{3 + 2 i}{- 2 + i} (i i i) \frac{1}{(2 + i)^{2}} (i v) \frac{1 - i}{1 + i} (v) \frac{(2 + i)^{3}}{2 + 3 i} (v i) \frac{(1 + i) (1 + \sqrt{3 i})}{1 - i} (v i i) \frac{2 + 3 i}{4 + 5 i} (v i i i) \frac{(1 - i)^{3}}{1 - i^{3}} (i x) (1 + 2 i)^{- 3} (x) \frac{3 - 4 i}{(4 - 2 i) (1 + i)} (x i) (\frac{1}{1 - 4 i} - \frac{2}{1 + i}) (\frac{3 - 4 i}{5 + i}) (x i i) \frac{5 + \sqrt{2 i}}{1 - \sqrt{2 i}}$