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Relationship Between Addition And The Modulus Of A Complex Number

Solve: |z|+2=5.

z=-1, 3

z=2, 3

z=3, -3

Solve: $\left|x^2-4\right|=3$ .

x=-1,1

x=-2/3, -4

x=-5/3, -1

Solve: x+2=|2x+3|.

x=-1, 2

x=-2/3, -4

x=-5/3, -1

Solve: |3x-3|=3/2.

x=-1

x=-2

x=1/2

Solve: |2x+2|=x+4.

x=-1, 2

x=-2, 2

x=-5/3, -1

Solve: |x+1|=4.

x=-1

x=3

x=2i

Solve: |z+10|=5.

z=-i

z=-2i

z=-5

Is the sentence true or false?
z=5 is the solution of 3|z-1|-1=11.

True

False

Solve: |x-1|=|2x+3|.

x=-1, 2

x=-2/3, -4

x=-5/3, -1

Solve: |x-6|=|x|.

x=-1

x=-2

x=3