Learn how to express complex numbers in the standard form a + bi, where a and b are real numbers and i = √-1. This video covers 3 examples, showing you step-by-step how to multiply, divide, and simplify complex number expressions to achieve the a + bi form. Perfect for complex number beginners!
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𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Express (1+2i)(-2+i) in form a+ib, a b ∈ R = √-1. State the value of a and b.
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
To express z = (1+2i)(-2+i) in the form a+ib, we need to multiply the two complex numbers:
z = 1(-2) + 1(i) + 2i(-2) + 2i(i)
z = -2 + i - 4i + 2i^2
Recall that i^2 = -1. Substitute this into the expression:
z = -2 - 3i + 2(-1)
z = -2 - 3i - 2
z = -4 - 3i
Therefore, the complex number is in the form a + ib where a = -4 and b = -3.