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P. (9+11 i)^(2)

P. (9+11i)2 (9+11 i)^{2}

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Full solution

Q. P. (9+11i)2 (9+11 i)^{2}
  1. Calculate Squared Complex Number: To square the complex number (9+11i)(9 + 11i), we will use the formula (a+bi)2=a2+2abi−b2(a + bi)^2 = a^2 + 2abi - b^2, where a=9a = 9 and b=11b = 11. Calculation: (9+11i)2=92+2⋅9⋅11i−112(9 + 11i)^2 = 9^2 + 2\cdot9\cdot11i - 11^2
  2. Calculate a2a^2: Now we will calculate each part of the expression separately.\newlineFirst, calculate a2a^2 which is 929^2.\newlineCalculation: 92=819^2 = 81
  3. Calculate 2abi2abi: Next, calculate 2abi2abi which is 2×9×11i2\times9\times11i.\newlineCalculation: 2×9×11i=198i2\times9\times11i = 198i
  4. Calculate −b2-b^2: Finally, calculate −b2-b^2 which is −112-11^2.\newlineCalculation: −112=−121-11^2 = -121
  5. Combine Calculated Parts: Combine all the calculated parts to get the final result.\newlineCalculation: 81+198i−121=(81−121)+198i=−40+198i81 + 198i - 121 = (81 - 121) + 198i = -40 + 198i

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