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Chapter 8: Q. 578 (page 856)

In the following exercises, simplify.

i255

Short Answer

Expert verified

The simplified form is-i.

Step by step solution

01

Step 1. Given information.

The given imaginary number isi255.

02

Step 2. Simplify the power.

We know that,

i=-1i2=-1i3=-ii4=1

Divide the power by 4and rewrite,

localid="1646857845922" i255=i4路63+3=i463路i3=163路i3=1路i3=-i

Therefore, the simplified form islocalid="1646857833477" -i

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Most popular questions from this chapter

In the following exercises, solve.

5x-6=8

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In the following exercises, solve.

2x3=-2

Explain whyx4=x2{"x":[[79,82,83,87,91,93,93,95,97,99,100,103,103,104,104,104,105,106,109,116,127,145,161,175,183,186,187],[106,107,108,109,110,111,113,115,118,121,122,126,128,128,128,127,124,119,115,114,112,112,111,111,110,110,110],[141,138,135,134,132,130,129,128,128,128,129,130,132,134,137,142,145,148,149,150,151,151],[119,120,123,129,133,136,137],[153,154,154,156,156,157,157,157,157,157,157,156,156,156,156,156,156,156,156,156,156,156,155,154,152,150,149,149,148,149,149,154,162,170,178,179,180,180,179],[185,186,186,187,191,194,197,199,200,201],[183,184,185,189,195,202,206,208],[229,230,232,236,239,244,249,252,254,256,256,256,255,252,250,249,248,247,245,242,240,238],[264,264,262,261,261,261,260,260,260,260,260,261,262,264,268,272,281,286,289,289,289],[245,246,250,259,269,279,288,289,290,291],[277,281,281,282,283,283,283,283,283,283,283,282,285,289,296,303,308,309,309]],"y":[[105,107,109,112,115,116,117,112,103,93,81,69,55,48,45,44,44,43,42,41,40,38,35,32,31,29,29],[71,71,71,70,70,69,68,68,68,68,68,70,74,78,83,88,92,95,97,98,98,99,99,98,96,94,92],[65,65,68,71,75,79,83,87,89,92,96,98,101,104,105,105,105,103,101,99,98,97],[83,83,83,83,83,83,83],[52,53,54,57,61,66,70,75,76,77,76,74,71,66,62,59,57,56,55,54,53,52,52,54,58,60,62,63,64,64,65,65,65,63,62,60,60,61,61],[87,87,86,85,85,84,84,84,84,84],[98,97,97,96,95,94,92,92],[66,66,65,65,65,65,67,70,73,77,82,87,91,95,97,98,99,99,99,99,97,97],[66,65,65,67,70,73,78,82,86,90,93,95,97,98,99,99,98,95,93,92,91],[85,85,85,84,83,81,81,81,81,81],[49,49,50,50,52,56,58,60,62,63,64,64,65,65,65,64,63,62,63]],"t":[[0,26,43,60,76,94,126,159,177,193,209,227,243,260,276,292,309,327,343,359,376,392,409,426,442,459,475],[942,947,959,975,1000,1043,1059,1075,1092,1108,1125,1142,1159,1175,1192,1209,1225,1242,1259,1275,1292,1308,1345,1363,1375,1392,1399],[1736,1791,1807,1824,1842,1858,1875,1891,1908,1924,1941,1958,1974,1991,2008,2025,2041,2058,2074,2091,2108,2123],[2491,2520,2540,2557,2574,2590,2607],[3144,3217,3225,3239,3256,3272,3289,3305,3323,3388,3409,3424,3439,3455,3472,3489,3506,3522,3540,3556,3573,3605,3656,3672,3689,3705,3722,3739,3755,3899,3904,3922,3939,3955,3972,3988,4005,4107,4110],[4450,4455,4471,4488,4504,4521,4538,4554,4571,4607],[4831,4854,4870,4888,4904,4921,4937,4954],[5378,5403,5420,5437,5453,5470,5487,5503,5520,5537,5554,5570,5587,5604,5620,5636,5653,5671,5687,5704,5720,5724],[6030,6086,6102,6119,6136,6153,6170,6186,6202,6219,6237,6252,6270,6286,6303,6319,6336,6352,6370,6386,6391],[6718,6752,6769,6786,6802,6819,6836,6852,6868,6885],[7431,7441,7447,7453,7468,7485,7501,7518,7534,7551,7584,7601,7651,7668,7684,7701,7717,7734,7850]],"version":"2.0.0"}. Then explain whyx16=x8{"x":[[108,111,115,118,123,128,129,131,133,136,139,144,146,147,147,147,148,150,151,153,157,164,176,196,217,241,254,258,259],[177,179,181,185,188,192,195,197,199,200,200,199,193,185,178,172,170,169,168],[241,239,234,229,222,216,211,208,205,204,204,204,205,209,217,226,236,245,251,254],[189,190,194,203,211,216,218,218],[249,250,250,250,250,249,249,248,248],[270,269,268,267,266,265,265,265,265,265,265,267,268,270,273,276,278,280,280,280,280,280,280,278,277,274,271,270,270,269,269,269],[295,298,303,312,321,327,330,331],[303,304,307,311,314,318,320,322,323],[347,349,353,359,363,365,367,368,368,365,361,360,359,358,359],[387,386,383,378,373,367,364,361,360,360,360,362,369,374,380,383,384,384],[347,348,349,351,361,372,382,388,390],[403,404,407,410,411,413,414,414,415,415,413,410,408,406,406,406,405,405,405,407,408,409,411,412,412,412,412,412,409,407,405,404,403,403,402,401,401,401,401,401,401,403,405]],"y":[[170,170,173,175,179,182,184,184,180,173,162,145,129,112,96,83,74,70,69,68,68,68,68,68,68,66,64,63,63],[118,118,116,116,116,116,116,119,124,130,137,144,151,156,159,161,161,161,161],[110,110,112,115,120,126,132,138,143,148,152,155,157,158,159,159,156,152,149,148],[137,137,137,137,137,137,137,138],[75,77,80,86,90,95,99,101,103],[70,70,70,72,75,80,85,89,93,97,98,101,102,102,102,101,99,97,95,94,91,90,89,88,87,87,87,87,88,88,89,90],[121,121,121,121,120,119,118,118],[143,143,143,143,142,141,141,141,141],[111,111,110,110,111,115,119,125,134,140,143,145,145,140,136],[104,104,105,109,114,119,125,129,133,136,138,140,141,141,140,138,136,135],[127,126,126,126,125,124,123,122,122],[85,85,84,84,84,84,85,88,92,95,99,102,105,107,109,110,111,112,113,113,113,113,112,110,108,105,103,100,99,97,96,95,95,94,94,92,91,90,88,86,85,84,84]],"t":[[0,50,67,83,100,117,133,150,199,216,233,249,267,284,299,316,334,350,366,383,400,417,434,449,466,484,500,516,534],[1057,1065,1082,1099,1116,1132,1148,1165,1183,1200,1216,1232,1249,1265,1282,1299,1316,1333,1371],[1674,1682,1698,1715,1731,1748,1765,1782,1799,1815,1831,1849,1865,1881,1898,1915,1932,1948,1965,1975],[2386,2414,2431,2448,2464,2481,2497,2549],[2961,3014,3030,3047,3063,3080,3097,3113,3129],[3496,3523,3533,3546,3563,3579,3596,3613,3629,3647,3663,3680,3696,3713,3729,3746,3762,3779,3796,3813,3830,3846,3862,3879,3896,3913,3930,3945,3962,3979,3995,4012],[4562,4567,4578,4596,4612,4628,4645,4661],[4950,5023,5044,5062,5078,5096,5111,5127,5135],[5454,5461,5477,5494,5511,5527,5544,5561,5577,5594,5610,5627,5644,5694,5707],[5900,5910,5926,5943,5960,5977,5994,6010,6027,6043,6060,6076,6094,6109,6127,6143,6160,6163],[6436,6441,6445,6460,6477,6493,6510,6526,6543],[6953,6960,6975,6992,7009,7025,7042,7059,7076,7093,7108,7125,7142,7159,7175,7193,7209,7225,7247,7259,7276,7292,7308,7325,7342,7358,7375,7392,7408,7425,7441,7459,7515,7524,7541,7558,7575,7593,7608,7625,7643,7658,7669]],"version":"2.0.0"}.

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