Take your complex number skills to the next level! This video covers more advanced examples of expressing complex numbers in the standard form a + bi. We'll show you step-by-step how to handle combinations of multiplication, division, powers of i, and other operations to simplify complex number expressions and achieve the a + bi form. Perfect for complex number practice!
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๐๐ฎ๐๐ฌ๐ญ๐ข๐จ๐ง: Express z = (2+i)/(3-i)(1+2i) in form a+bi and find the value of a and b.
๐๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง:
z = (2+i) / ((3-i)(1+2i))
Denominator: (3-i)(1+2i) = 3 + 6i - i - 2i^2 = 3 + 5i + 2 = 5 + 5i
z = (2+i) / (5+5i)
Multiply by conjugate: ((2+i)(5-5i)) / ((5+5i)(5-5i))
Numerator: 10 - 10i + 5i - 5i^2 = 10 - 5i + 5 = 15 - 5i
Denominator: 25 - 25i^2 = 25 + 25 = 50
z = (15 - 5i) / 50 = 15/50 - (5/50)i = 3/10 - (1/10)i
a = 3/10, b = -1/10