Write left bracket, 7, plus, 3, i, right bracket, squared(7+3i) 2 in simplest a, plus, b, ia+bi form.
Question
Write left bracket, 7, plus, 3, i, right bracket, squared(7+3i) 2 in simplest a, plus, b, ia+bi form.
Solution
To square a complex number, we use the formula (a + bi)^2 = a^2 + 2abi - b^2.
Here, a = 7 and b = 3.
Step 1: Square a: a^2 = 7^2 = 49
Step 2: Multiply a and b by 2: 2ab = 2 * 7 * 3 = 42
Step 3: Square b: b^2 = 3^2 = 9
Step 4: Substitute a^2, 2ab, and b^2 into the formula: (a + bi)^2 = a^2 + 2abi - b^2 (7 + 3i)^2 = 49 + 42i - 9
Step 5: Simplify the equation: (7 + 3i)^2 = 40 + 42i
So, (7 + 3i)^2 in simplest a + bi form is 40 + 42i.
Similar Questions
Simplify the expression to a + bi form:left bracket, minus, 2, plus, 2, i, right bracket, minus, left bracket, minus, 7, plus, 7, i, right bracket(−2+2i)−(−7+7i)
Express left bracket, x, plus, 7, right bracket, squared(x+7) 2 as a trinomial in standard form.
Simplify the expression to a + bi form:left bracket, 8, plus, 8, i, right bracket, left bracket, 12, minus, 10, i, right bracket(8+8i)(12−10i)
Simplify the expression to a + bi form:left bracket, minus, 1, minus, i, right bracket, minus, left bracket, 3, plus, 5, i, right bracket(−1−i)−(3+5i)
Express as a complex number in simplest a+bi form:start fraction, 13, plus, 7, i, divided by, minus, 3, minus, 10, i, end fraction−3−10i13+7i
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.