(3 + 4*i*)^{2} = -7 + 24*i*

|3 + 4*i*|^{2} = |-7 + 24*i*|

|3 + 4*i*| = 5; |-7 + 24*i*| = 25

[And 5^{2} = 25]

(3 + 4*i*)^{3} = -117 + 44*i*

|3 + 4*i*|^{3} = |-117 + 44*i*|

|3 + 4*i*| = 5; |-117 + 44*i*| = 125

[And 5^{3} = 125]

1 more...and I'll change the 1st complex number this time!

(8 + 7*i*)^{4} = -12,319 + 3,360*i*

|8 + 7*i*|^{4} = |-12,319 + 3,360*i*|

|8 + 7*i*| = the square root of 113; |-12,319 + 3,360*i*| = 12,769

[And the 4th root of 12,769 = the square root of 113 because 113^{2} = 12,769]

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