Number and algebraCourse skill

Powers of - using a graphing calculator

Evaluate a power of in calculator complex-number mode, then check the result against the four-step cycle.

  • Select complex-number mode and use the calculator’s special key. Enter the power using brackets where needed.
  • Read the answer in Cartesian form. For these integer powers, the answer is exactly or .
  • The useful check is and : positive powers repeat .
  • If a display contains a tiny rounding residue, use the cycle to identify the exact value.

Example 1

Calculate, then check

Use a GDC in complex-number mode to evaluate the power. Check your result using the cycle.

Enter this expression in complex-number mode.Optional check using the four-step cycle.

Example 2

Calculate, then check

Use a GDC in complex-number mode to evaluate the power. Check your result using the cycle.

Enter this expression in complex-number mode.Optional check using the four-step cycle.

Remember
AI HL specifies technology for powers of complex numbers in Cartesian form. The cycle is a useful check on the calculator result; sums, differences, products and quotients also require by-hand skills.

Your turn

Question 1

Use a GDC in complex-number mode to evaluate the power. Check your result using the cycle.

Check answer
Enter this expression in complex-number mode.

Enter the displayed power using the key in complex mode. Check the output against the cycle , −1, −, 1.

Question 2

Use a GDC in complex-number mode to evaluate the power. Check your result using the cycle.

Check answer
Enter this expression in complex-number mode.

Enter the displayed power using the key in complex mode. Check the output against the cycle , −1, −, 1.

Question 3

Use a GDC in complex-number mode to evaluate the power. Check your result using the cycle.

Check answer
Enter this expression in complex-number mode.

Enter the displayed power using the key in complex mode. Check the output against the cycle , −1, −, 1.

Question 4

Use a GDC in complex-number mode to evaluate the power. Check your result using the cycle.

Check answer
Enter this expression in complex-number mode.

Enter the displayed power using the key in complex mode. Check the output against the cycle , −1, −, 1.

Question 5

Use a GDC in complex-number mode to evaluate the power. Check your result using the cycle.

Check answer
Enter this expression in complex-number mode.

Enter the displayed power using the key in complex mode. Check the output against the cycle , −1, −, 1.

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