Question

If (2 + 3i)2 + (2 − 3i)2 = a + bi, a = and b =

Answer 1

Given:

If (2 + 3i)2 + (2 − 3i)2 = a + bi

Required:

a = and b =

Step-by-step explanation:

`\begin{gathered} \left(2+3i\right)\cdot \:2+\left(2-3i\right)\cdot \:2=a+bi \\ \\ expand\text{ the term} \\ \\ 8=a+bi \\ \\ rewrite\text{ 8 in the standard complex form 8+0}\iota \\ \\ 8+0i=a+bi \\ \\ \mathrm{Complex\:numbers\:can\:be\:equal\:only\:if\:their\:real\:and\:imaginary\:parts\:are\:equal} \\ \\ Rewrite\:as\:system\:of\:equations: \\ \\ \begin{bmatrix}8=a\\ 0=b\end{bmatrix} \\ \\ a=8,\:b=0 \\ \end{gathered}`

Required answer:

a=8, b=0