Examples of simplifying complex numbers.Examples of simplifying complex numbers.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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To simplify the expression when a complex number a + ib is being divided by c + id, we use the following steps:

Expression to be simplified: (a + ib)/(c + id)

Multiply numerator and denominator by conjugate of denominator

[(a + ib)(c - id)]/[(c + id)(c - id)]

=> [(a + ib)(c - id)]/(c^2 - i^2*d^2)

=> [(a + ib)(c - id)]/(c^2 + d^2)

The numerator can be simplified by opening the brackets and multiplying the terms.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To simplify the complex number raised to square, we'll expand the square, using the formula:

(a+b)^2 = a^2 + 2ab + b^2

We'll put a = 13 and b = 14i:

(13 + 14i)^2 = 13^2 + 2*13*14i + (14i)^2

(13 + 14i)^2 = 169 + 364i + 196i^2

Since i^2 = -1, we'll get:

(13 + 14i)^2 = 169 + 364i - 196

We'll combine the real parts:

(13 + 14i)^2 = -27 + 364i

The simplified form of the complex number raised to square is:

(z)^2 = -27 + 364i, where z = 13 + 14i

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