Simplify complex expr
Perform the indicated operations and write the results in the form of a + bi:
(2 + 3i)³ (ii) (1 + i)⁴
(2 + 3i)³ (ii) (1 + i)⁴
Correct answer:
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Dr Math
Some semi-results:
(2+3i) * (2+3i) = 2 * 2 + 2 * 3i + 3i * 2 + 3i * 3i = 4+6i+6i+9i2 = 4+6i+6i-9 = 4- 9 +i(6 + 6) = -5+12i
(-5+12i)*(2+3i) = (-5+12i) * (2+3i) = -5 * 2 + (-5) * 3i + 12i * 2 + 12i * 3i = -10-15i+24i+36i2 = -10-15i+24i-36 = -10- 36 +i(-15 + 24) = -46+9i
(1+i) ^ 2 = (1+i) * (1+i) = 1 * 1 + 1 * i + i * 1 + i * i = 1+i+i+i2 = 1+i+i-1 = 1- 1 +i(1 + 1) = 2i
(2+3i) * (2+3i) = 2 * 2 + 2 * 3i + 3i * 2 + 3i * 3i = 4+6i+6i+9i2 = 4+6i+6i-9 = 4- 9 +i(6 + 6) = -5+12i
(-5+12i)*(2+3i) = (-5+12i) * (2+3i) = -5 * 2 + (-5) * 3i + 12i * 2 + 12i * 3i = -10-15i+24i+36i2 = -10-15i+24i-36 = -10- 36 +i(-15 + 24) = -46+9i
(1+i) ^ 2 = (1+i) * (1+i) = 1 * 1 + 1 * i + i * 1 + i * i = 1+i+i+i2 = 1+i+i-1 = 1- 1 +i(1 + 1) = 2i
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