Question

Multiply the complex numbers: (1∕2 + 4i)2

Answer 1

Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to complex numbers (1∕2 + 4i)².

Define complex numbers.

Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the case of quadratic equations, the unknown roots are simplified using complex numbers if the roots are not real. In computer science and engineering, complex numbers are used. Both mechanical and civil engineering use complex numbers. Control systems employ complex numbers.

Given,

Complex numbers:;

(1/2 + 4i)²

(a +b )² = a² + b² + 2ab

Multiplying,

(1/2)² + (4i)² + 2(1/2)(4i)

1/4 + 16i² + 4i

i² = -1

1 - 64/4 + 4i

-63/4 + 4i

Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to (1∕2 + 4i)².

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