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Complex Numbers Calculator - Online Calculator - Tutorpace

# Complex Numbers Calculator

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Complex numbers are the numbers of the form ‘a + bi’ where, ‘a’ and ‘b’ are real numbers and ‘i’ is the imaginary number. The value of ‘i’ is i = √-1 and it is an imaginary number. Therefore, a complex number is a combination of the real number part and the imaginary number part and they can be computed using operations such as addition, subtraction, multiplication and division. Complex numbers calculator is the online tool which can be easily simplify and evaluate complex numbers.

Example 1:Multiply the given two complex numbers: (1 + 2i) (2 + 3i)

(1 + 2i) (2 + 3i) = (1* 2) + (1 * 3i) + (2i * 2) + (2i * 3i)

This gives: 2 + 3i + 4i + 6i2

Simplifying the above expression by combining the like terms, we get: 2 + (3i + 4i) + 6i2

This gives: 2 + 7i + 6i2

The value of i = √-1 ==>i = -1

So we get: 2 + 7i + (6 * -1) ==> 2 + 7i – 6

This simplifies to: 7i – 4

Example 2: Simplify the given expression: 4/ (3 – i)

To simplify the given expression, we should multiply the numerator and the denominator by the conjugate of (3 – i) which is (3 + i).

This gives: [4 * (3 + i)]/ [(3 – i) * (3 + i)]

This gives: (12 + 4i)/ (9 – i2)

The value of i = √-1 ==>i = -1

This implies: (12 + 4i)/ (9 – (-1)) ==> [4 * (3 + i)]/ 10 = [2 * (3 + i)]/ 5

Simplifying further we get: (6 + 2i)/ 5