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Properties Of The Modulus Of A Complex Number

Let z1 =1+i, z2 =3+2i, then calculate, |z1+z2|.

Is the sentence true or false?

∣2+3i+4+5i∣=∣8+6i∣\left|2+3i+4+5i\right|=\left|8+6i\right|.

Is the sentence true or false?

Let z1 =5+i, z2 =6+3i, |z1+z2| =4.

Let z1 =5+2i, z2 =3i, then calculate, |z1+z2|.

Is the sentence true or false?

Let z1 =1+2i, z2 =-i, |z1|+|z2| =5\sqrt{5} +1.

Is the sentence true or false?

Let z1 =-2+i, z2 =3-i, |z1+z2| =1.

Let z1 =1+i, z2 =3+2i, then calculate, |z1|+|z2|.

Is the sentence true or false?

∣(8+7i)+(6+5i)∣ ≤ ∣8+7i∣+∣6+5i∣\left|\left(8+7i\right)+\left(6+5i\right)\right|\ \le\ \left|8+7i\right|+\left|6+5i\right|.

Complete:

Given that ∣Z∣+2∣Ẕ∣=15\left|Z\right|+2\left|Ẕ\right|=15, then ∣2Ẕ3∣=\left|2Ẕ^3\right|=__________.