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Write (2+3i)^(3) in simplest a+bi form. Answer:

Write (2+3i)3 (2+3 i)^{3} in simplest a+bi a+b i form.\newlineAnswer:

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Write (2+3i)3 (2+3 i)^{3} in simplest a+bi a+b i form.\newlineAnswer:
  1. Expand Expression: Expand (2+3i)3(2+3i)^{3} using the binomial theorem or by multiplying (2+3i)(2+3i) by itself three times.\newline(2+3i)3=(2+3i)×(2+3i)×(2+3i)(2+3i)^{3} = (2+3i) \times (2+3i) \times (2+3i)
  2. First Multiplication: Multiply the first two factors (2+3i)(2+3i) and (2+3i)(2+3i).(2+3i)×(2+3i)=4+6i+6i+9i2(2+3i) \times (2+3i) = 4 + 6i + 6i + 9i^2Since i2=−1i^2 = -1, we can simplify this to:4+12i−94 + 12i - 9= −5+12i-5 + 12i
  3. Second Multiplication: Multiply the result from Step 22 by the remaining (2+3i)(2+3i).\newline(−5+12i)×(2+3i)=−10+24i−15i+36i2(-5 + 12i) \times (2+3i) = -10 + 24i - 15i + 36i^2\newlineAgain, since i2=−1i^2 = -1, we can simplify this to:\newline−10+24i−15i−36-10 + 24i - 15i - 36\newline=−46+9i= -46 + 9i

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