Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 60

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If $z_{1} = - 3 + 5 i; z_{2} = - 5 - 3 i$ and $z$ is a complex number lying on the line segment joining $z_{1} & z_{2},$ then $a r g (z)$ can be

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Important Questions on Complex Numbers

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 61

If

(1 + i) z = (1 - i) \bar{z}

, then

z

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 62

Let

z

and

ω

be two non-zero complex numbers such that

|z| = |ω|

and

a r g z = π - a r g ω,

then

z

equals

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 63

If

z_{1}

and

z_{2}

are two non-zero complex numbers such that

|\frac{z_{1}}{z_{2}}| = 2

and

\arg (z_{1} z_{2}) = \frac{3 π}{2},

then

\frac{{\bar{z}}_{1}}{z_{2}}

is equal to -

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 64

Number of complex numbers

z

such that

|z| = 1

and

|\frac{z}{\bar{z}} + \frac{\bar{z}}{z}| = 1

is

(a r g (z) \in |0, 2 π|)

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 65

lf

|z_{1}| = |z_{2}|

and

\arg (\frac{z_{1}}{z_{2}}) = π,

then

z_{1} + z_{2}

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 66

The number of solutions of the system of equations

Re (z^{2}) = 0, |z| = 2

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 67

If

|z^{2} - 1| = {|z|}^{2} + 1,

then

z

lies on

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 68

If $| z - 2 i | + | z - 2 | \geq | |z| - | z - 2 - 2 i | |,$ then locus of $z$ is