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Conjugate of a Complex Number

If Z 1 = a+...

Question

If $Z_{1} = a + i, a \neq 0 a n d Z_{2} = 1 + b i, b \neq 0$ are such that $z_{1} =_{2}$ then-

A

a = 1, b = 1

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B

a = 1, b = - 1

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C

a = - 1, b = 1

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D

a = - 1, b = - 1

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Solution

The correct option is A $a = 1, b = - 1$
$z_{1} = a + i z_{2} = 1 + b i {¯ z}_{2} = 1 - b i ⟹ a + i = 1 - b i a = 1, b = - 1$

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Similar questions

z_{1} = \frac{1}{a + i}, a \neq 0

z_{2} = \frac{1}{1 + b i}, b \neq 0

z_{1} = {¯ ¯ ¯ z}_{2}

z_{1} = \frac{1}{a + i}, a \neq 0

z_{2} = \frac{1}{1 + b i}, b \neq 0

z_{1} = {¯ z}_{2}

Q. If a and b are real numbers between 0 & 1 such that the points

z_{1} = a + i, z_{2} = 1 + b i

z_{3} = 0

form an equilateral triangle, then find

a

b

a

b

are real numbers between

0

1

such that the points

z_{1} = a + i, z_{2} = 1 + b i

z_{3} = 0

from an equilateral triangle then

a

b

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