Boost your complex number skills! This video covers a variety of examples of expressing complex numbers in the standard form a + bi. We'll show you step-by-step how to handle multiplication, division, and combinations of operations to simplify complex number expressions and achieve the a + bi form. Perfect for complex number practice!
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๐๐ฎ๐๐ฌ๐ญ๐ข๐จ๐ง: Express z = (1+i)/(1-i) in form a+bi and find the value of a and b.
๐๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง:
z = (1+i) / (1-i)
Multiply by conjugate: ((1+i)(1+i)) / ((1-i)(1+i))
Numerator: 1(1) + 1(i) + i(1) + i(i) = 1 + i + i + i^2 = 1 + 2i - 1 = 2i
Denominator: 1^2 - (i)^2 = 1 - (-1) = 1 + 1 = 2
z = 2i / 2 = i = 0 + 1i
Therefore, a = 0 and b = 1.