Complex Number Division Formula

Complex Number Division Formula

A Complex number is in the form of a+ib, where a and b are real numbers the ‘i’ is called the imaginary unit. The imaginary number, i, has the property, such as

i2
 =
−1
.

To find the division of any complex number use below-given formula.

Let two complex numbers are a+ib, c+id, then the division formula is,

a+ibc+id=ac+bdc2+d2+bc−adc2+d2i

Solved Examples

Question 1: Divide the complex roots.
7–6i2–3i

Step 1 –

7−6i2−3i×2+3i2+3i

Step 2 –

14+21i−12i−18i24+6i−6i−9i2

Step 3 –

14+21i−12i−18(−1)4+6i−6i−9(−1)

=

14+21i−12i+184+6i−6i+9

Step 4 –

32+9i13

Step 5 –

3213+913i

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