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The Reciprocal Of A Complex Number

Fill in the blank:
Let z₁, z₂, are complex numbers. Then, $\left|\left(3+2i\right)-\left(1+2i\right)\right|$ ≥ ________.

$\left|\left(3+2i\right)\right|-\left|\left(1+2i\right)\right|$

$\left|\left(3+2i\right)\right|$

$\left|\left(1+2i\right)\right|$

Is the sentence true or false?
Let z=5, is complex number then $Re\left(z\right)=\left|z\right|$ .

True

False

Fill in the blank:
$\left|\left(2+3i\right)^5\right|=$ _______.

$\left(\right|2+3i\left|\right)^5$

$\left(5\right|2+3i\left|\right)^5$

both

Fill in the blank:
Let z₁, z₂, are complex numbers. Then, | $\frac{\left(1+2i\right)}{\left(3+4i\right)}$ | =________.

$\left|\left(1+2i\right)\right|-\left|\left(3+4i\right)\right|$

$\left|\left(1+2i\right)\right|\left|\left(3+4i\right)\right|$

$\frac{\left|\left(1+2i\right)\right|}{\left|\left(3+4i\right)\right|}$

Is the sentence true or false?
Let z=2+3i, is complex number then 3 ≤ |z|.

True

False

Is the number sentence true or false?
|z|=|z|.

True

False

Fill in the blank:
$\left|\left(3+2i\right)+\left(1+2i\right)\right|$ ≤ ________.

$\left|\left(3+2i\right)\right|$

$\left|\left(1+2i\right)\right|$

$\left|\left(3+2i\right)\right|+\left|\left(1+2i\right)\right|$

Fill in the blank:
Let z₁, z₂, are complex numbers. Then, $\left|\left(1+2i\right)\left(3+4i\right)\right|=$ ________.

$\left|\left(1+2i\right)\right|-\left|\left(3+4i\right)\right|$

$\left|\left(1+2i\right)\right|\left|\left(3+4i\right)\right|$

$\left|\left(1+2i\right)\right|+\left|\left(3+4i\right)\right|$

Is the sentence true or false?
Let z₁, z₂, are complex numbers then the distance between the two points z₁ and z₂ in complex plane is |z₁-z₂|.

True

False

Is the number sentence true or false?
$\left|-z\right|=\left|z\right|$ .

True

False

Questions

Time

Score

The Reciprocal Of A Complex Number

Fill in the blank:Let z1, z2, are complex numbers. Then, ﻿∣(3+2i)−(1+2i)∣\left|\left(3+2i\right)-\left(1+2i\right)\right|∣(3+2i)−(1+2i)∣﻿ ≥ ________.

﻿∣(3+2i)∣−∣(1+2i)∣\left|\left(3+2i\right)\right|-\left|\left(1+2i\right)\right|∣(3+2i)∣−∣(1+2i)∣﻿

﻿∣(3+2i)∣\left|\left(3+2i\right)\right|∣(3+2i)∣﻿

﻿∣(1+2i)∣\left|\left(1+2i\right)\right|∣(1+2i)∣﻿

Is the sentence true or false?Let z=5, is complex number then ﻿Re(z)=∣z∣Re\left(z\right)=\left|z\right|Re(z)=∣z∣﻿.

True

False

Fill in the blank:﻿∣(2+3i)5∣=\left|\left(2+3i\right)^5\right|=∣∣​(2+3i)5∣∣​=﻿ _______.

﻿(∣2+3i∣)5\left(\right|2+3i\left|\right)^5(∣2+3i∣)5﻿

﻿(5∣2+3i∣)5\left(5\right|2+3i\left|\right)^5(5∣2+3i∣)5﻿

both

Fill in the blank:Let z1, z2, are complex numbers. Then, |﻿(1+2i)(3+4i)\frac{\left(1+2i\right)}{\left(3+4i\right)}(3+4i)(1+2i)​﻿| =________.

﻿∣(1+2i)∣−∣(3+4i)∣\left|\left(1+2i\right)\right|-\left|\left(3+4i\right)\right|∣(1+2i)∣−∣(3+4i)∣﻿

﻿∣(1+2i)∣∣(3+4i)∣\left|\left(1+2i\right)\right|\left|\left(3+4i\right)\right|∣(1+2i)∣∣(3+4i)∣﻿

﻿∣(1+2i)∣∣(3+4i)∣\frac{\left|\left(1+2i\right)\right|}{\left|\left(3+4i\right)\right|}∣(3+4i)∣∣(1+2i)∣​﻿

Is the sentence true or false?Let z=2+3i, is complex number then 3 ≤ |z|.

True

False

Is the number sentence true or false?|z|=|z|.

True

False

Fill in the blank:﻿∣(3+2i)+(1+2i)∣\left|\left(3+2i\right)+\left(1+2i\right)\right|∣(3+2i)+(1+2i)∣﻿ ≤ ________.

﻿∣(3+2i)∣\left|\left(3+2i\right)\right|∣(3+2i)∣﻿

﻿∣(1+2i)∣\left|\left(1+2i\right)\right|∣(1+2i)∣﻿

﻿∣(3+2i)∣+∣(1+2i)∣\left|\left(3+2i\right)\right|+\left|\left(1+2i\right)\right|∣(3+2i)∣+∣(1+2i)∣﻿

Fill in the blank:Let z1, z2, are complex numbers. Then, ﻿∣(1+2i)(3+4i)∣=\left|\left(1+2i\right)\left(3+4i\right)\right|=∣(1+2i)(3+4i)∣=﻿________.

﻿∣(1+2i)∣−∣(3+4i)∣\left|\left(1+2i\right)\right|-\left|\left(3+4i\right)\right|∣(1+2i)∣−∣(3+4i)∣﻿

﻿∣(1+2i)∣∣(3+4i)∣\left|\left(1+2i\right)\right|\left|\left(3+4i\right)\right|∣(1+2i)∣∣(3+4i)∣﻿

﻿∣(1+2i)∣+∣(3+4i)∣\left|\left(1+2i\right)\right|+\left|\left(3+4i\right)\right|∣(1+2i)∣+∣(3+4i)∣﻿

Is the sentence true or false?Let z1, z2, are complex numbers then the distance between the two points z1 and z2 in complex plane is |z1-z2|.

True

False

Is the number sentence true or false?﻿∣−z∣=∣z∣\left|-z\right|=\left|z\right|∣−z∣=∣z∣﻿.

True

False

Incorrect

Great!

Fill in the blank:
Let z₁, z₂, are complex numbers. Then, $\left|\left(3+2i\right)-\left(1+2i\right)\right|$ ≥ ________.

$\left|\left(3+2i\right)\right|-\left|\left(1+2i\right)\right|$

$\left|\left(3+2i\right)\right|$

$\left|\left(1+2i\right)\right|$

Is the sentence true or false?
Let z=5, is complex number then $Re\left(z\right)=\left|z\right|$ .

Fill in the blank:
$\left|\left(2+3i\right)^5\right|=$ _______.

$\left(\right|2+3i\left|\right)^5$

$\left(5\right|2+3i\left|\right)^5$

Fill in the blank:
Let z₁, z₂, are complex numbers. Then, | $\frac{\left(1+2i\right)}{\left(3+4i\right)}$ | =________.

$\left|\left(1+2i\right)\right|-\left|\left(3+4i\right)\right|$

$\left|\left(1+2i\right)\right|\left|\left(3+4i\right)\right|$

$\frac{\left|\left(1+2i\right)\right|}{\left|\left(3+4i\right)\right|}$

Is the sentence true or false?
Let z=2+3i, is complex number then 3 ≤ |z|.

Is the number sentence true or false?
|z|=|z|.

Fill in the blank:
$\left|\left(3+2i\right)+\left(1+2i\right)\right|$ ≤ ________.

$\left|\left(3+2i\right)\right|$

$\left|\left(1+2i\right)\right|$

$\left|\left(3+2i\right)\right|+\left|\left(1+2i\right)\right|$

Fill in the blank:
Let z₁, z₂, are complex numbers. Then, $\left|\left(1+2i\right)\left(3+4i\right)\right|=$ ________.

$\left|\left(1+2i\right)\right|-\left|\left(3+4i\right)\right|$

$\left|\left(1+2i\right)\right|\left|\left(3+4i\right)\right|$

$\left|\left(1+2i\right)\right|+\left|\left(3+4i\right)\right|$

Is the sentence true or false?
Let z₁, z₂, are complex numbers then the distance between the two points z₁ and z₂ in complex plane is |z₁-z₂|.

Is the number sentence true or false?
$\left|-z\right|=\left|z\right|$ .