Multiplying and Dividing Complex Numbers (Leaving Cert Mathematics): Flashcards

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Multiplying and Dividing Complex Numbers
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Value of i2i^2

−1-1

Notation for conjugate of zz

z‾\overline{z}

How to find conjugate of a+bia + bi

Change sign of imaginary part only

Type of number result from z+z‾z + \overline{z}

Real number

Type of number result from z×z‾z \times \overline{z}

Real number

Value of i1i^1

ii

Value of i3i^3

−i-i

Value of i4i^4

11

Repeating cycle pattern for powers of ii

i,−1,−i,1i, -1, -i, 1

How to divide complex number by real number

Divide each term separately

Method to divide by complex number

Multiply by conjugate of denominator

Standard form for complex number answers

a+bia + bi

Conjugate of 3−4i3 - 4i

3+4i3 + 4i

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